I have been wondering about it as well. He is already Viscount Granger, Baron of Ryde, Knight of the Most Honorable Order of the Bath, Governor and Constable of Windsor Castle, Colonel of His Britannic Majesty's Marines. While his services are undoubtfully relevant, they are probably not enough to earn an advancement in peerage, even if Caroline works for it, at least without disclosing some of what they are doing and planning in Russia to the general public. He most likely cannot get another Order, since Garter is very exclusive and have limited number of members (my guess is that he would only get it if his father died), he is not Scottish and has no connection with Scotland - so Thistle is out, and classes for advancements in the Order of the Bath were only created in 1815. And George was already captain to one of their biggest frigates, so although he loathes the idea of being bound to a fleet in a ship-of-the-line, that might be a possibility.
One can only hope that instead they give him command of a frigate squadron, and let him play havoc in the Mediterranean or the Caribbean. He is young so all the captains need to made Post after him. We can only imagine what he would do if they give him Calvert, Roberts, and maybe others like Brookstone or Lord Barnfield (I think Lennox is a flag captain in a ship-of-the-line, right?). They know him so well that it would probably be the frigate version of Nelson's "mind-reading" captains that fought on the Nile.
PS: what happened to HMS Belvidera? It needed a profound refit, but that was several years ago, so it should be functional and it was a good and fast ship. George never encounter it again. Maybe some of his people will get it.