Hang on to cold fish (5)
I believe the answer is:
cling
'hang on to' is the definition.
(thesaurus)
'cold fish' is the wordplay.
'cold' becomes 'C' (abbreviation, eg on taps).
'fish' becomes 'ling' (ling is a kind of fish).
'c'+'ling'='CLING'
(Other definitions for cling that I've seen before include "Hold on tightly, refuse to abandon" , "Adhere, hold tight" , "Stick close (to surface)" , "Adhere to - ring" , "Keep hold" .)