Atletico Madrid will face with bigger challenge from Barcelona but I don't think Real Madrid will become stronger in the new season. I think they will become weaker than in the past one. No big transfer and they lost two main central defenders (Ramos and Varane) and only have one replacement (Alaba)
the departure of ramos and varane from madrid certainly left a big hole in their defense, even though real madrid have got Alaba but it looks like it is not enough to strengthen madrid defense next season, in my opinion barcelona and athletico madrid are two clubs that will challenge for the la league title this season forward and honestly I really doubt that next season Real Madrid will be able to compete with these two teams, moreover it looks like Real Madrid really don't want to add new players this year's transfer season and no player has been linked with Real Madrid this season apart from Kylian Mbappe and me think financial constraints are a problem for real madrid this year so it doesn't strengthen their squad.
Left big hole for Real Madrid after missing two great defender Sergio Ramos and Raphael Varane because they have give more impressive performance for Real Madrid, now only got David Alaba and many still bigger problem for Real Madrid right now but still not any planning to get new player. I think not sure Real Madrid can speak more with La Liga or champion league.