Noticed this doesn't specify when Gatekeep joins so I thought I would provide an answer. They will join after the timeskip in new game plus under the following conditions: - You have completed 2 of the house's stories on the same save - Your current house is the final house you have not finished

I started with Scarlet Blaze, finished Azure Gleam, and then started up Golden Wildfire and once I hit the timeskip gatekeeper was waiting to be recruited.