Follower gives woman record (5)
I believe the answer is:
sheep
'follower' is the definition.
(sheep can mean an unquestioning follower)
'woman record' is the wordplay.
'woman' becomes 'she' ().
'record' becomes 'EP' (abbreviation for extended play record).
'she'+'ep'='SHEEP'
'gives' acts as a link.
(Other definitions for sheep that I've seen before include "Timid followers" , "Woolly quadruped" , "Farm animal" , "Woolly animals" , "Easily led people" .)