Yeah, I think he will keep his pride aside immediately he is in Real Madrid, because he knows that the team can do without him, instead he is the one that needs the team to improve himself and win trophies, if possible set new records for himself. Ancelotti is a coach that every player respects and wants to make happy because he is a good and friendly coach, so his influence will humble Mbappe.
Sometimes, relationship matters alot. Maybe in PSG, he does not like some players and the coach, or he feels that he is bigger than them which is making him to fool himself, he will not try that in Madrid because there are young vibrant players in competition with him.
That's not certain, it all comes back to each person's character because so far we have seen Mbappe who is very selfish at PSG and if he is not able to change this then he will not be able to develop.
Indeed, so far we can see that Real Madrid is much bigger than the players, even though they are the best players in the world, because this team has implemented that no player is much bigger than the team, because of what happened in the past with all the star players. This is indeed the case and Mbappe also hopes that this will happen.