It was a sudden impulse. She had those a lot.
Clara knew the Doctor didn't like hugs. But how was she supposed to help it? There were so many feelings, such intense emotions she felt for this man, such a strong bond between these two. Not being able to express that, not even once in a while, felt like torture to her. Words were never their strength, though. Clara had a hard time expressing her feelings because it meant letting her guard down. She wasn't afraid of doing that per se – she had no reason to be, not in front of the Doctor, the only person in the universe she really trusted. The problem was that she knew he had problems with expressing his emotions as well, and his were probably bigger than hers. How would he react? She knew the Doctor loved her, but how would he be able to talk about it? Clara already felt guilty for all the times she had hugged him even though he was clearly uncomfortable. There was no way she would overwhelm him with just randomly telling him how much he meant to her.

Words. Only one way of communicating in this universe filled with endless definitions of the word 'language'. Since they couldn't use that one, they gifted each other little things all the time. Tiny, insignificant things which started to carry so much worth as soon as they were given to the other, more worth than any diamond in the world. Whenever they did that they would look each other in the eyes for a few seconds and smile, before explaining what exactly that gift was. Every time, during those seconds, they knew. They could just feel the bond, the warmth they both brought out in each other. It didn't matter if the gift was just a small stone one of them picked up along the way, it was never about the material stuff itself. It was about the feeling. This was their way of showing each other affection. Sometimes the Doctor would brush it off and playfully call Clara's gift 'stupid' or 'useless', but Clara just smiled, because she knew. Plus, most of the time her gifts really were stupid or useless. But that didn't matter to either of them.

Right there in the TARDIS such a moment had passed with Clara showing him the picture on the phone, to which he reacted weirdly. It was different than usual. Was that why Clara felt like it wasn't enough? All she knew was she was standing behind the Doctor and she felt a sudden impulse to hug him. She wanted to feel the connection between them, wanted to actually touch him to feel it even more. She wanted to feel close to him. So she broke the hugging rule, once again, and did it. But she didn't feel bad about it. She knew she wouldn't, something told her the Doctor wouldn't mind this time. After all, he did hug her rather enthusiastically earlier. And fact was, the reason the Doctor didn't like hugs was because they were a good way to hide the face, but now? Their relationship was so strong and solid now, they knew they would always be alright as long as they could count on each other. There was no reason to hide faces anymore. This was the right time, this was an intimate moment.

She was proven right as she hugged him from behind and he put his hand on her arm in response. They both just stayed like that for a while, smiling because they were so close to each other. Clara could stay right there, in this position, forever. The Doctor couldn't, evidently as he turned around. For a few seconds Clara thought he wanted to let go, but she was surprised to find out he actually stayed in her arms and just wanted to face her. He then put his arms around her as well. Clara could actually hear his two hearts beat, given she wasn't exactly the tallest person. Every second of it was beautiful.
She put her head up to find the Doctor looking at her. Their eyes met. "Thank you", he said. Clara laughed, which caused the Timelord to smile softly. "What for?"
"The hug."
"I never thought, not in a million years, that you would ever thank me for giving you a hug."
"Well," he laughed, "I am just full of surprises."
She looked at him smiling and he looked right back. Their adoring gazes mirrored each other's feelings perfectly.
"I want to thank you as well," Clara said, "for letting me. And for actually hugging me back. That really tops every surprise. Best gift I've ever received."
For a few seconds they stood there in silence, soaking up the joy of being this close. They both knew this wasn't something that would happen every day. Both of them being willing to be that open with each other at the same time was rare. They treasured this moment.
"There is no one else in the universe I'd rather hug, Clara. In fact there isn't anyone else I would hug at all. Ever."
Clara laughed as she let go of him, knowing that sadly this couldn't last forever and they should stop before it got too awkward for one of them. It was okay. She was satisfied, and so was he.
"Oh, you're quite the charmer today, aren't you?" she said as she put her focus back on the TARDIS control, excited about whatever their next destination would be.
The Doctor smiled at her wit and her laughing and her jokes, all the qualities he adored so much. Most of all, he was glad to see her happy and alive.
"I've missed you, Clara Oswald."