Wow! So Beautiful. Do you think they'd hug or would one of them ruin it by asking 'What the hell took you so long?' or 'what are you wearing? And are you crying? You are such a girl Merlin!' Lol, sorry. In my mind, Arthur always ruins their reunions simply by being himself, lol. I suppose they would could start with simply staring at each other before saying 'Idiot' and 'Prat'. Actually, I quite like that idea, lol, must remember to write that up one day. Anyway, completely beautiful! Makes me smile while also making me somewhat sad still!
I kinda see it as more of a mushy affair that neither would ruin because they're both too much in shock; Merlin from not really believing that Arthur has finally returned that he must be dreaming this as he so often has in the past and Arthur because he can't believe how much Merlin has changed and how old he looks though he hasn't aged a day. I feel like they would just stare for a while and then I would say Arthur would run to Merlin and pull into a hug. It would be a bone crushing hug, and Merlin would just stand there and try to wrap his mind around the fact that it is Arthur in the flesh. Merlin wouldn't hug back just yet, he would start to feel his eyes water up and his body starting to go limp as he lets the years just push him down to the ground and Arthur would gently follow with arms still wrapped around Merlin. Merlin would then hesitantly wrap his own arms around Arthur and they would simply hug each other and reacquaint each other with the sounds of their breathing and their smell. Then Merlin would say "It's been so long" and Arthur would comfort him with soothing words and rubbing of his back in small circles.
I know, I want one so bad! There are too many loose ends that they've just left tangling, that need to be finished and tied into the tapestry that is Merlin or else the fans will be left empty and forever filled with grief! Ok, so a tad melodramatic but you get my point.