Gloucester's got a big job: Lord Protector of England. And this means he basically runs the kingdom until Henry VI is old enough. It's a lot of responsibility to run a kingdom, and it's even more complicated if you're doing it for someone else. You know—someone who's not even in kindergarten yet, but will one day be your king.
Is Gloucester the man for the job? He probably is. He's sensible—look how often Henry asks his advice once he gets old enough, and look how solid it usually is—plus he's loyal and responsible. He does have a long-running feud with Winchester, who says Gloucester is ambitious and wants all the power for himself. But of the two, Gloucester is usually first to make peace, and his language is much less fierce, especially when you consider that Winchester often threatens to kill him.
Gloucester may not be quite the Obi-Wan Kenobi of Henry VI, Part 1, but he's still a pretty decent guy. Lots of Lord Protectors are tempted to take over, but while Gloucester may enjoy power, he is trying to do his best for Henry.