Happy let into Police Department (7)
I believe the answer is:
pleased
'happy' is the definition.
(synonyms)
'let into police department' is the wordplay.
'let' becomes 'lease' (as in to lease or let a building).
'into' is an insertion indicator.
'police department' becomes 'PD' (abbreviation eg in NYPD, New York Police Dept).
'lease' placed into 'pd' is 'PLEASED'.
(Other definitions for pleased that I've seen before include "like Punch?" , "Content" , "Glad" , "Gratified" , "Feeling satisfaction" .)