An Ex-Shaolin Monk works as a Private Investigator in 1920?s New York. When he accepts a new murder case he find his past and present colliding and the only way to solve the case is to solve the mystery of his past.

Better to prioritize clarity over mystification in a logline, because the nondescript “…mystery of his past.” doesn’t evoke intrigue rather confusion with regards to the action the MC needs to take.

The whole ex-shaolin monk thing seams like a hook and it is in my mind quite an interesting combo. A super martial arts expert fighting bad guys during prohibition sounds good.
But it seams to be missing an antagonist and also if the genre is film noir then perhaps clarify this with a mention of the potential femme-fatale as well. This may help with the wording in the beginning of the logline that seams cumbersome:

1920’s NYC, When an ex Shaolin monk and now a PI is approached by a beautiful woman to find her father’s murderer. He must rely on his skills to fight his way through organized crime and police corruption to catch the killer.

Hope this helps.