Bigheaded fool, but a natural swimmer (4)
I believe the answer is:
bass
'a natural swimmer' is the definition.
'bass' can be an answer for 'swimmer' (bass is a kind of fish). I am unsure of the 'a natural' bit.
'bigheaded fool' is the wordplay.
'bigheaded' becomes 'b' (this might be a standard abbreviation I've not previously seen).
'fool' becomes 'ass' (both can mean a stupid person).
'b'+'ass'='BASS'
'but' is the link.
Can you help me to learn more?
(Other definitions for bass that I've seen before include "Large percussion instrument" , "Very low - perch" , "Big percussion instrument" , "bottom of sound?" , "Lowest male singer" .)