Policeman’s information American woman takes in rapidly at first (8)
I believe the answer is:
gendarme
'policeman's' is the definition.
(gendarme is a kind of policeman)
'information american woman takes in rapidly at first' is the wordplay.
'information' becomes 'gen' (gen can informally mean information).
'american woman' becomes 'dame' (informal US term for a woman).
'takes in' means one lot of letters goes inside another.
'at first' indicates taking the first letters.
The first letter of 'rapidly' is 'r'.
'dame' enclosing 'r' is 'darme'.
'gen'+'darme'='GENDARME'
(Other definitions for gendarme that I've seen before include "French officer - merge DNA (anag)" , "Force man" , "see in Paris!" , "...French fuzz!" , "French Connection cop" .)