The next new episode of “Supergirl” is titled “Ace Reporter”, the 18th episode of Season 2, and is scheduled to air on Monday, April 24.
Beyond that we know that episode 19 of Season 2 is titled “Alex” and will air on Monday, May 1. After that is an episode titled “City of Lost Children”, which will focus heavily on James Olsen and the challenges he faces as The Guardian, and will air on The CW on May 8.
Therefore, that leaves a 21st episode to air on May 15 before the Season Finale on May 22, making up the complete 22 episode run of Season 2.
The CW has already renewed “Supergirl” for a third season.