Stick with cold swimmer (5)
I believe the answer is:
cling
'stick' is the definition.
(I know that stick can be written as cling)
'with cold swimmer' is the wordplay.
'with' means one lot of letters go next to another.
'cold' becomes 'C' (eg on taps).
'swimmer' becomes 'ling' (ling is a type of fish).
'c'+'ling' is 'CLING'.
(Other definitions for cling that I've seen before include "Hold on as for dear life" , "Hold on tightly, be dependent" , "Hold tightly, become attached" , "act like limpets" , "Stick close (to surface)" .)