Take a swim in city close to seaside (5)
I believe the answer is:
bathe
'take a swim' is the definition.
(I've seen this before)
'city close to seaside' is the wordplay.
'city' becomes 'bath' (I've seen this before).
'close to' suggests the final letters (the close/ending of).
The last letter of 'seaside' is 'e'.
'bath'+'e'='BATHE'
'in' is the link.
(Other definitions for bathe that I've seen before include "Swim or paddle" , "Swim in sea" , "Wash, soak" , "Wash; swim" , "Take dip in sea" .)