Persistent criminal's beat, facing time (8)
I believe the answer is:
constant
'persistent' is the definition.
(thesaurus)
'criminal's beat facing time' is the wordplay.
'criminal's' becomes 'cons' (abbreviation for 'convict').
'beat' becomes 'tan' (I've seen this before**).
'facing' says to put letters next to each other.
'time' becomes 't'.
'cons'+'tan'+'t'='CONSTANT'
(Other definitions for constant that I've seen before include "Changeless and unceasing" , "Resolute" , "Endless" , "sustained" , "exactly as before" .)