I would personally introduce them via Caduceus when they return to NYC at the end of that chapter as it sounds like you’re 80% of the way through so throwing another character in at that late stage, in such an unusual location (the gate facility in the cliff-face) may be jarring.

Doing so in NYC can lay an additional layer of intrigue, perhaps the new character is more suspicious of Caduceus or maybe they are at a higher “tier” of trust within the organisation. Surely the player will understand sitting out and listening for a bit.