Big admirer (3)
I believe the answer is:
fan
'big admirer' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for fan that I've seen before include "Zealot" , "Manual cooling device - for admirer?" , "Enthusiastic admirer as of pop star" , "Devoted admirer or air cooler" , "Spanish women wave it to cool themselves" .)