Stella Adler began as an actress, but she was best known as an acting instructor and founder of the Stella Adler Studio of Acting. She had studios in both New York and Los Angeles. Lots of big names went there for training -- Marlon Brando, Warren Beatty, Harvey Keitel in NYC and Nick Nolte, Salma Hayek, Sean Astin in LA. Adler taught in both locations, though mainly in NYC.
Barry and Claire Brook were well established music professors in the NYC academic world and I'm sure they were among Adler's many friends in Manhattan. http://www.pendragonpress.com/claire_brook.php
Neat card! I bet she had an assistant type up a bunch of these to keep in touch various old friends.