DISCLAIMER:Any theory that is posted is just in fun. I am posting these as a reader myself, imagining I'm in your shoes and what you would think. None of these theories have potential spoilers in them and can be taken how you want to take them. They may or may not be true, but that's up to you to decide.
The Grand Maester is an old man, so old one would expect him to stay away from the affairs of politics but apparently not. He is not what he seems.
-The Grand Maester is presented as frail and somewhat sickly, he drops the scroll of the declaration of war when giving it to Aeyron and he walks hunched over and with a limp. But several times he has been "caught lacking", 'When Jade left, the Grand Maester’s frailness seemed to say goodbye and leave as well.'-whenever he's been "caught lacking" he immediately defaults back into the frail and sick old man but those times he has been caught napping he appears to be moving normally.
-This is most apparent in the chapter after The Battle of King's Landing when he appears to Ignis Swyft who's in his bed recovering. He comes to Ignis praising his work but again reminding him of Rhaenerys Blackfyre, about 10 chapters prior he mentions Rhaenerys and her dragons. It isn't a coincidence he's talking about her even now.
-His fragile appearance may be a deceiving tool for his means to bring Rhaenerys to King's Landing and possibly the throne, maybe he is a Blackfyre sympathiser.
-“I urge the king to put aside Lady Joanna, reach a means of peace with the enemy and send a marriage pact to Rhaenerys Blackfyre” the Grand Maester advised becoming more passionate about it.' It appears clear that the Grand Maester has an obsession with Rhaenerys and it'll be interesting to see in the future books whether he will actively try to get Rhaenerys to King's Landing and potentially the throne.