Madrid dominance in La Liga may not be disturbed, because their eternal rival Barcelona cannot do much in the transfer window, apart from that Hansi Flick certainly needs to adapt in his first season. Even this season, without striker No. 9, Ancelotti managed to bring Madrid to three trophies at once. Of course, the addition of Mbappe will make Ancelotti fleet not only dominate La Liga, but also the Champions League.
Madrid is now stronger than ever succeeding to bring in Mbappe to their squad. Madrid with their former squad without addition of the new players conquered Laliga and champions league combined, there is absolutely no reason to believe now that they will seize to dominate the domestic league and UCL respectively when there's additional top scorer to the squad. It's possible for them to be outshined someday but I don't see that happening anytime soon because Barcelona who is the closest rival is not in good shape right now to compete with a squad that has Vini, Bellingham, Modric and Mbappe as the number 9. Coming to champions league, it has always been very dreadful for teams to play Real madrid including the big clubs in their respective domestic league. Now, they have been on disadvantage and Madrid will become more fearful to play with. This coming season will be more exciting to watch as there are various developments in various teams including change of couch and addition of new players.