Hello back in the new year with a new chapter!
Thank you to ginar369 who helped me with a very good idea for this chapter! I appreciate your help, thanks again! :-)

Jaime

In the following week, Jaime and the people who'd saved him sent several letters to issue some warnings. To the couple's family and friends, but mostly to Winterfell. They needed to make sure, the people there would know about the Wildlings who'd attacked them and also had killed their own people.
He wrote the letter in person to Lady Sansa Stark:

"Lady Sansa,
I'm writing you in the knowledge that you will handle the following information with caution. As you know, Tormund Giantsbane and a few of his men went out, looking after me. They found me, but only hours later we were attacked by other Wildlings, who didn't join the fight against the Night King. I'm sorry for I can not name you the clan they belong. I couldn't even describe their look, but I hope you'll have some people of the North in Winterfell who will recognize my inadequate description. Also, you need to know, they attacked us and killed all of Tormund's men. They took the dead bodies with them. I'm sorry for I can not tell you what they did with the dead bodies. Also, I have to thank Tormund, he saved my life at this day. He managed to rescue me but got killed too, which I feel very sorry for. He's buried here, for we could save his body. At this time, I'm recovering with the help from a family of your house. As soon as I'm able to travel, I will join Lady Brienne in Tarth.
Ser Jaime Lannister"

They sent the raven the same day, and Jaime hoped the people from Winterfell would be able to protect the North from more harm. Since the war was over, the North was still recovering from it, whole Westeros did the same to be true. The world didn't need some jackasses, killing other people.
But he couldn't think about that right now, he'd done what he'd been able to and now needed to concentrate on his physical recovering. He wanted to reunite with his woman. Wanted to finally meet his daughter, he was very curious about the little girl, who for sure wasn't that small anymore.
So he trained every day as much as possible, ate as much as he was able to and as soon as Jaime was allowed to walk he trained even more. It took him many weeks to get his strength back, but he wasn't as healthy as he'd been before. He still limped and needed a cane to stabilize him as he walked, but he refused to wait any longer. As much as his leg would hurt on his journey, it would have time to fully heal at Tarth.
And when the day came, where he left the family who'd saved him, gave him food and helped him to recover, he just took the money he would need for traveling and left the rest of it with them. They would need it much more, and he was grateful for their help. He had to promise them to send a raven as soon as he would reach Tarth to let them know he arrived safely.
He was able to find an old horse at a tavern on his travel to the next harbor where he would be able to get a ship to Tarth. It made the journey much more straightforward, for he didn't need to walk on his own. They traveled very slowly, but finally, he reached the harbor. Jaime sold his horse and used the rest of the money for the next best ship, which would sail to Tarth.
In the following evening, they left the harbor and Jaime were glad about it. Soon, he would be able to meet Brienne again.

Joanna

Every day she and her grandfather went to the harbor to check on the ships which had arrived. With every passing week, she grew more and more eager with her dad's arrival. Would he come at all? She so desperately wanted to finally meet him.
"Be patient with your father," her grandfather told her.
"He will come, it just takes some more time than we thought it would."
Joanna sighed and nodded when she suddenly saw a ship on the horizon as they walked back to their home. Against her will, she grew excited. Maybe he was on this ship.
"Can we please wait for just this one, grandpa?" She asked her grandfather, reaching for his hand.
"Sure we can, sweetheart, maybe this is our lucky day," her grandfather said patiently, and she smiled gratefully at him. She loved her grandfather with all her heart and was lucky that he went with her, was so patient with her. They walked back to the harbor where they waited for another hour until the ship reached them.
"It's a ship from the north! Can you see it?!" She realized excited, seeing the flag on the ship. Joanna squeezed her grandfather's hand and tried to pull him with her, but he stopped her.
"Let's wait here, we have the best view from here, for we can see the people leaving the ship," he insisted, and Joanna thought about it for a while until she nodded.
"Alright," she agreed then. Even if she wanted to be closer to the ship, she knew her grandfather was right. So she kept watching the people leaving the ship.
It wasn't many people leaving the ship, and when she finally thought no one would follow them, a man left the ship. He was limping and walking on a cane. He had long-grown blonde hair and a beard. She could even see some grey hair in his beard. He was skinny and looked around like he didn't know where to go. Joanna observed him, feeling something stir inside her. The man felt familiar to her.
"Grandpa...," she whispered, squeezing his hand. "Do you think it is him?" She watched that man, who suddenly looked in their direction.
Joanna then knew it was him, she didn't understand why she just knew it was her father, so she let go of his grandfather's hand and walked towards the man, who was still looking at her. She stopped right in front of him. Joanna stared in what seemed her own green eyes, it was then when the girl finally realized it was him. She felt like she was complete for the first time of her life.
"Dad?" She whispered, staring at him, waiting for a response. When she didn't get one, she asked something more.
"Are you my father?" She couldn't hide her excitement as the man smiled at her.
"If you would tell me your name, little lady, I would surely be able to answer your question," he answered her with a bit of a hoarse voice, and Joanna liked him even more.
"I'm Joanna Lannister," she answered with a clear and proud voice, stretching her back which caused the man in front of her to smirk a bit.
"Joanna...," the man said with a soft smile on his lips.
Suddenly, she felt a hand on her shoulder and turned her head around to see her grandfather standing behind her.
But she turned her head back to her the man in front of her, still waiting for his answer. She stared at him, sometimes she wasn't very patient, so she asked again.
"Are you my father? Are you Jaime Lannister?"
The man, who had looked at her grandfather looked back at her again, and after a moment, he nodded slowly.
"Yes on both sides," he answered and stumbled as Joanna threw herself at him to give him a big hug around his waist.
"I knew you would come home today!" She whispered in excitement, hugging him as close around his waist, as she was able to. After a few moments, she felt his hands around her too. It was, besides being snuggled up to her mom, the best feeling in the whole world. Closing her eyes in happiness, she enjoyed the excitement of finally meeting her dad.

Brienne

She sat outside her room on the small balcony, trying to rest while her father and daughter were gone to the harbor. Many weeks had passed since they'd heard from Jaime and she didn't know what took him that long. No one had mentioned his physical status besides the fact that he'd been badly hurt.
Trying not to get impatient with him she sighed and decided to focus on a book instead. Brienne wasn't allowed to do some sparring for at least one more week. She couldn't wait for more conditional training again. It cleared her mind and made her calm down even more.
After a few more moments on trying to focus on the book, she placed it on the table beside her, not realizing that the door to her room had opened. Staring at the sea, she didn't hear the man coming inside, leaning on a cane. Also, she overheard him coming towards the entrance to the balcony, where she was sitting at.
A knock on the doorframe suddenly brought her attention back from the sea she'd been watching to the here and now. She turned her head to see a man standing in the doorframe. Hadn't she seen him before with this long beard and the poor condition, she would never have recognized him. Her eyes grew wide, and she stood up abruptly.
"Jaime?" She asked, not believing that he indeed was standing right in front of her. "Is that really you?"
"My lady," he just answered, and she felt her knees becoming weak only by hearing his voice. He looked exhausted and thinner than she remembered him. As he came outside to be a bit closer to her, she realized how badly he was limping. Overwhelmed with questions and emotions, she just stared at his appearance in front of her. She couldn't say one word.
"Brienne?" Jaime asked, looking at her in confusion. He was delighted to see her again, she could read it all over his face. And she was too, she just couldn't handle all her emotions running through her, making her feel awful. Suddenly he seemed to realized what exactly was her problem, so he came close on his own, put the cane aside and pulled her into his arms without asking more questions. Feeling him, pulling her into his embrace, made her realize she was holding her breath. Letting out a heavy sigh she finally was able to move again, so she brought her arms around Jaime as well, leaning herself against him, inhaling his scent.
"You're really here," she whispered after a moment, now fully believing it was him, Jaime Lannister, who held her in his arms.
"I am. Sorry, that it took too long. I'm a slow walker these days," he told her with a low voice, still holding her in his lovingly embrace.
"I know the both of you were waiting eagerly." Brienne could hear the amused tone in his voice, which caused her to look up to him. "Both of you?" She asked curiously.
"Our daughter just happened to be at the harbor as I arrived," he explained to her, and she finally was able to show him a smile.
"She'd been waiting there every day since your letter arrived," she said, still enjoying his embrace. For such a long time she'd missed this, missed him and everything about him. Now they probably would be able to have time on their own.
"She told me, don't know where she got it from, but she's a great talker, don't you think?" He asked with amusement and love in his voice which caused Brienne to smile again.
"She is wonderful, isn't she?" Never in her whole life, Brienne had thought herself as a mother, but she realized, she enjoyed it more than most things.
"She is," Jamie answered and kissed her forehead first, then, softly, her lips.
"Is missed you Brienne of Tarth," he said then, and suddenly, Brienne felt tears burning in her eyes.
"I missed you too, Ser Jaime," she whispered in a hoarse voice, looking in his eyes. She saw so much love for her in these, it made her speechless. Brienne would never have imagined that both of them would genuinely have a chance. And now, that Cersei Lannister was dead, they could be together without being afraid.
They kissed each other again, still holding each other's embrace, enjoying their company. They only walked inside to sit down on Brienne's bed, for she knew Jaime needed some rest, he was exhausted, she could see it written all over his face. So they just laid down on her bed, snuggling up against each other. Brienne leaned her head against Jaime's chest, listening to his steady heartbeat, while he caressed her upper arm.
Tomorrow, there would be enough time to talk about what happened to them, after they'd lost each other in the great war. Tonight, Brienne and Jaime would just enjoy to finally be together, the feeling of each other. They would stay awake for a long time, kissing each other, sharing a few loving words. Later, their daughter would join them for the night. They would welcome her in their arms. They would enjoy being together, listen to Joanna's stories, so she and her father would be able to get to know each other better. Brienne enjoyed every second of being together with Jaime and Joanna - with her family.
At one point all of them fell asleep, snuggled up to each other.