Are Ainz and his servants still leveling in the New World? Are Ainz and his servants still leveling up the same way they were when they were killing monster to get exp in Yggdrasil?
Hmmm... To my understanding, Ainz and the high-tier minions (read those that are level 100) don't level up any further, as they are maximum level already. It's never mentioned that they 'get stronger' while others like the lizardmen and that weird hamster indeed do (the narrative comments several times that they are training to get stronger). Now, it is possible the New World has a higher level cap but insofar it hasn't been mentioned at all in the nine LN, the WNs nor the anime and manga.
So Ainz ain't levelling nor are the floor guardians, but some of his minions do.