Racy novel about woman's sport (7)
I believe the answer is:
archery
'sport' is the definition.
(archery is a kind of sport)
'racy novel about woman's' is the wordplay.
'novel' indicates an anagram (letters in a new or novel order).
'about' means one lot of letters goes inside another.
'woman's' becomes 'her' (belonging to a woman).
'racy' anagrammed gives 'arcy'.
'arcy' placed around 'her' is 'ARCHERY'.
(Other definitions for archery that I've seen before include "The sport of shooting arrows with a bow" , "Arrow-shooting" , "Sport of the bowman" , "Bowman's sport" , "Toxophily" .)