Look at what cat’s got - they might be fluttering (9)
I believe the answer is:
eyelashes
'what cat's got they might be fluttering' is the definition.
The definition suggests an adverb but the answer is not.
'look at' is the wordplay.
'look' becomes 'eye' (eyeing is a kind of looking).
'at' becomes 'lashes' (I can't justify this - if you can you should believe this answer much more).
'eye'+'lashes'='EYELASHES'
Can you help me to learn more?
(Other definitions for eyelashes that I've seen before include "ocular features" , "They can flutter" , "Facial hairs" , "Facial features" , "they're on the lids" .)