Extra turns can still be created while Ugin's Nexus is on the battlefield. They're not skipped until they would begin, so if Ugin's Nexus leaves the battlefield before that happens, the extra turns will be unaffected.

An "extra turn" is any turn created by a spell or ability. Notably, it doesn't include additional turns taken in tournaments after time expires for a round.

Notably, if you control more than one Ugin's Nexus, all but one will be exiled and an extra turn created for each. If the Ugin's Nexus that remains on the battlefield isn't on the battlefield when each of those extra turns would begin, you can take those turns.