Green’s Dictionary of Slang

beat n.2

[SE beat, to overcome; note WWI milit. my beat, my girlfriend]

1. [mid-19C–1900s] (US) an outstanding person, one who defeats all rivals; usu. as the beat of..., the equal of...

2. [mid-19C–1910s] an outstanding object, an incomparable circumstance; usu. as the beat of..., the equal of...

In phrases

get a beat on (v.)

[mid-19C+] (US) to have at a disadvantage.