The Adventurer's League FAQ states that characters with sufficient experience must advance at the next opportunity.

When do characters advance in level? [...]

Characters with sufficient experience must advance at the next opportunity: the end of an episode of a multi-part adventure such as D&D Encounters or a published adventure, after a D&D Expedition, or after a long rest. The language indicating that a character can advance after a session is incorrect and will be corrected in future editions of the Player's Guide.

(Emphasis and excerpting added to highlight relevant bits.)

Vizeran DeVir, a drow archmage is common to both Princes of the Apocalypse and Out of the Abyss. In the former,

he was the one responsible for creating the 4 Elemental Weapons wielded by the 4 prophets, the main antagonists of the campaign. In the latter, he plays a role in the endgame of the campaign by providing a way for the heroes to destroy/banish the demon lords.

Another thread you could use to link the two campaigns is that the Fane of the Eye in PotA was built by ancient Ghaunadaur worshiping drow. Some say that the demon lord Juiblex is actually an aspect of Ghaunadar. What if instead of

being turned into an ocre jelly, touching the statue in area F19 of the Fan of the Eye (potA p.121), you were teleported to the Oozing Temple (OotA p.34). In any event ou can decide for yourself the relationship of these various entities and how Vizeran DeVir ties in with them.

As for "hidden stairs," as requested in your comment on another answer, I can point to a few between PotA and the Underdark.

1. Fane of the Eye, area F12. Abandoned Mine (PotA p.119) - mine tunnels lead into the Underdark.
2. The Black Geode, area G5. Underdark Entrance (PotA p.136.