Mbappé was suppose to leave the club this summer, he already had an agreement with Realmadrid and even rejected a move to the Saudi that came with huge offer of him earning a bigger salary and other financial benefits just to favour his plans of moving to Madrid, however PSG were forced to punish him, by stopping him from training with the Snr team and even increasing his release clause to keep other teams away from signing him, which made Mbappé to change his mind and sign a new deal, hoping they'll allow him leave next summer.
Well the new 1 year contract he signed this season includes that he'll be allowed to move to another club of his choice for the right price, therefore I don't think Mbappé would want to remain at the club no matter how they try to persuade him to stay, he'll probably move to Realmadrid next summer.
PSG have failed in past season, not able to comprehend matters and bringing in the very best performance on the pitch, but failed to represent an outstanding results outside Ligue One. I would suggest for PSG to throw more concern on signing young talents because depending on just one valuable player will actually see the team decline in performance in his absence. Kylian Mbappe is a big name for PSG and happens to be their most valuable player, the team wouldn't relent to allow him leave for free next summer, Nasser Al-Khelaifi will work out alternatives measures to improve Paris Saint Germain.