Resolute detectives in action (7)
I believe the answer is:
decided
'resolute' is the definition.
(resolute can mean decided or determined)
'detectives in action' is the wordplay.
'detectives' becomes 'CID' (abbreviation for Criminal Investigation Department).
'in' means one lot of letters goes inside another.
'action' becomes 'deed' (deed is a kind of action).
'cid' going inside 'deed' is 'DECIDED'.
(Other definitions for decided that I've seen before include "Came to a resolution" , "Made mind up, being unequivocal" , "Categorical" , "unmistakable" , "Determined; resolute" .)