Begins job after inmate leaves prison (4)
I believe the answer is:
jail
'prison' is the definition.
(jail can mean a prison)
'begins job after inmate leaves' is the wordplay.
'begins' suggests taking the first letters.
The first letters of 'job after inmate leaves' is 'JAIL'.
(Other definitions for jail that I've seen before include "(Send to) prison" , "sentence" , "Nick" , "having a stretch here?" , "Cooler" .)