Almost there.

I hope it's not too confusing. I brought the action to the end of season 7, but some (if not most) of the things that happened on the show haven't happened yet.
Broadly
- King's Landing and Winterfell (Lannisters and Starks) are locked in something of a cold war
- A Lannister is King (or Queen)
- Arya thinks that Sansa is married to Tyrion


I apologize for lifting a few lines from the show. I won't do it again. The words I want Arya and Sandor to tell one another haven't been written for these characters (but who knows, maybe Season 8 will not break my heart like Episode VIII did)

"Man is least himself when he talks in his own person. Give him a mask, and he will tell you the truth."

Oscar Wilde


Arya

Jon hugged her tightly. She held him just as fiercely. They had nearly lost each other a dozen times in their missions over the Wall, and yet going south into Westeros seemed just as dangerous.

"I wish I could tell them you are safe."

Arya's face seemed carved in stone.

Three years earlier, when she was a brand new recruit, the guilt would have burned through her, and tears would have stung her eyes.

Two years earlier, after she had first seen her black brothers die and after she had killed the first women and children in one of the wildlings' raids, she would have only felt a pang of guilt.

Now, after facing an army of wights and seeing the Night King, she hardly felt anything other than a vague warmth in her chest when she thought about the family she had left behind.

"Are you sure you don't want to come with me at Winterfell?"

"You know I can't. In King's Landing there's no one to know my face. Except Sansa, but she probably won't be at the meeting."

Would lady Sansa Lannister even recognize her sister under the tattered black cloak?

Jon pressed his forehead against hers. Arya closed her eyes. There was one other person in King's Landing who was at least an equal risk, but there was no point of telling her brother. And unlike the Imp's wife, the Hound was likely to be at the meeting.

"If Ser Jeor Mormont were alive, he'd have a better chance of getting through to the Lannisters. They might not forget that Ser Alliser Throne fought on House Targaryen's side during the Rebellion. If he fails, find Tyrion Lannister. He might be the only one to listen to you."

She nodded. No further than a few months earlier, she had believed that the White Walkers were stories to frighten children. They had to hope that the living dead would be enough to change the Lannisters' mindset about the war with the North.

She had to be on the delegation that took the wight to the Capital. She'd been in the ranging party that captured the wights. She was the fastest fighter in the entire Watch and she could handle close combat if they lost control of the dead. But mostly she was there for skill with the bow. She would be the one to shoot the obsidian arrow through it at the end of the demonstration.

"I'll do my part. You make sure Father believes you."

Her brother nodded. They shared a look full of hope that they would see each other again, but saying the words aloud invited bad luck. Too many brothers had died in recent months.

She watched Jon and Samwell Tarly load the casket containing a wight into their wagon and secure it. Sam sat next to the casket, and Jon mounted his horse.

On the other side of the courtyard, two men loaded an identical casket onto their wagon. Arry Snow, the smallest and fastest Ranger in the Night's watch took her place next to it.

Ser Alliser Thorne and the other men of the Night's Watched mounted their horses.

The Night's Watch was sending five men to go to Winterfell and ten men to King's Landing. Arya wondered if these fifteen would make a difference in case of an attack.

Part of her wanted to stay at Castle Black and face the next assault.


Sandor

King's Landing bore the marks of the Battle of Blackwater. Sandor Clegane might have reacted to the sight of the fire ravaged walls, but Sandor Clegane was no more. The man getting off the ship was no one. He was over six feet tall and his wavy hair flows freely past his shoulders. The setting sun gives it a reddish hue and a gust of wind uncovers a few white streaks.

A street vendor smiles at his handsome face. The man smiles back. He is a stranger in this land, but he has a mission. The Many Faced God was promised a name and the man has to fulfill that promise.

It took him a few days of drinking with cutthroats in taverns, working alongside tanners and blacksmiths, and begging in the streets to get the information he needed. When he was done, the grimy beggar limped into a passageway and on the other side Jaqen H'ghar walked with his back straight and his face clean.

The man used the memories of Sandor Clegane to navigate the maze of streets in Flea Bottom. He looked up, toward the Dragonpit atop Rhaenys's hill. He had caught the scent of his target, but he had to stalk it.

The man did not hurry. He would learn the rhythm of this strange city and at the right moment he would fulfill his contract.

A man had learned to wait.


Arya

She took her position in one of the walls of the Dragonpit. She made sure she had a direct line of fire to the casket and its surroundings. She watched Ser Alliser and the others set the perimeter. The big men from the Night's Watch prepared themselves.

Arya was relieved to see that Sansa was not in attendance. And neither was the Hound. She wondered briefly about his fate, but when the demonstration was about to start, she pushed away all other thoughts. The future of their world depended on how persuasive their demonstration was going to be.

Ser Alliser and the others showed the effects of fire and dragonglass. Arya put the arrow back in her quiver when the wight was neutralized. As agreed, she returned to the inn where they were staying and waited for the others.

Although she had done a fair bit of waiting in the freezing lands behind the Wall, Arya wasn't good at it. She nursed her mug of ale, watching the world go by from her corner of the tavern until she heard the commotion outside.

She ran with her hand on the hilt of her sword. The men of the Night's Watch were under attack, in a widening circle of frightened people. White cloaks were swarming the plaza, but the most damage was done by a mountain of a man. Ser Alliser's last blow knocked the helmet from the man's head revealing monstrous scars. Ser Alliser was on one knee, struggling to get back up.

Without a thought for her safety, Arya jumped in front of the old ranger and parried the killing blow. It knocked her on her ass, but she jumped back to her feet and charged the monster. He swatted her aside as a mere nuisance and raised his sword again, but before he could strike, a dart whooshed through the air, straight into his neck. He toppled forward, almost crushing Ser Allaiser.

Arya looked around, but she saw no one who had thrown the dart.


Sandor

When the highborns and their retinue left the Dragonpit, an old man with ragged clothes and an eye missing followed them.

They were too wrapped up in their important affairs to pay much attention to the beggar. Euron Greyjoy jerked his arm away from the dirty hand that dared to reach out to him. One of the beggar's fingers brushed the skin of Greyjoy's wrist before he fell to his knees. The piteous old man touched his forehead to the pavement. Euron kicked him hard with his steel boots as he passed by.

The beggar curled into a ball in a ditch. Unseen by human eyes, he took a small vial from the pouch around his neck and drank the blue liquid. The Many Faced God will have the death that was promised to him. The Long Farewell would make sure of it.

When the beggar stood up, he wore a different, more handsome face. He looked over the crowd with disinterested eyes. He knew these people like he knew this city. Vague memories of a man who was no one.

One memory though was not vague. One silhouette among all the others had crisp sharp edges. He followed it and watched it as it killed men in tattered black cloaks.

Another silhouette suddenly stood out from the ghostly scene in front of him. Even brighter than the monster, a slender figure stood before him. No one knew he should stay away. Sandor Clegane knew he had to kill one and protect the other. He threw a dart dipped in wolfsbane into his brother's neck and vanished in the crowd.

He was only a few steps away when his vision started to blurr. He steadied himself on the wall, and tried to find one of the safe places he had set up before darkness fell fully over his eyes. He knew the price one paid for taking a life that was not one's to take.

The City Watch arrested him and believing him drunk instead of blind, they gave him to someone who pushed him into a cart. When his vision came back, he was in a locked barred cell on the back of a wagon with two other men.

He tried to make sense of his surroundings and the people on the inside and on the outside of the bars. When they made camp, he addressed one of the young men who was gathering wood for the fire.

"Boy! Lovely boy!"

"What do you want?"

"A man has a thirst. A man does not drink for a day and a night. A boy could make a friend."