Green’s Dictionary of Slang

(US) an escape, usu. from prison.

1903		H. Hapgood Autobiog. of a Thief 326: The attendants were always eager to get hold of those notes, expecting to find news of beats (escapes) about to be attempted.
1949		Monteleone Criminal Sl. (rev. edn).
1950		Goldin et al. DAUL 24/2: Beat, n. [...] 3. An escape from prison or custody. ‘Phil the Fire-bug made a nice beat out of the bughouse (insane asylum).’.