They believe time served initially limits crime (7)
I believe the answer is:
theists
'they believe' is the definition.
(I've seen this before)
'time served initially limits crime' is the wordplay.
'initially' says to take the initial letters.
'limits' means one lot of letters goes inside another (limit can mean to contain or block off).
'crime' becomes 'heist' (heist is a kind of crime).
The initial letters of 'time served' is 'ts'.
'ts' enclosing 'heist' is 'THEISTS'.
(Other definitions for theists that I've seen before include "Believers" , "religious people" , "people who believe in God" .)