Their main target is definitely to defend the title, especially the Champions League title they won this season. That is a very realistic target for them considering they have a very good squad now, especially by bringing in Mbappe, it complements their shortcomings on the front line.
Mbappe, who during his time at Paris Sait Germain has not yet tasted a title, will certainly aim for the Champions League title with Real Madrid. Maybe it's true that it won't be easy, but if we compare the chances of him getting the Champions League title with Real Madrid, his chances are much greater than the chances of winning the Champions League with Paris Saint Germain.
He can complete that next season because Real Madrid is now in the first place on the list which in my opinion has a big chance of winning the Champions League next season.
Every team who got to win a trophy in the last season usually have a goal of defending the trophy they won and a chance to maintain the track record of retaining the trophy, few seasons back Madrid created history as they won the champions league title Three times in a row and somehow if they succeed in winning the champions league again in the new season, they may be on track to recreating a record the once hard and again for the second time they will be the only team with the highest champions league trophy record in the history of the champions league.
Having the PSG start to the Madrid squad ahs over the time brought about various speculations in the media about the improved strength expected of Madrid due to this particular signing and it has eve further caused so many stare that most persons confidently say the believe Madrid will win the champions league title again which I don't see to be impossible but still I wouldn't jump on the bandwagon of absoluteness at the chances Madrid has got, knowing what football can be, when the expected turns out the unexpected and several other things too can happen.