Believe it's a false start by a swimmer (4)
I believe the answer is:
feel
'believe' is the definition.
(feeling is a kind of believing)
'a false start by a swimmer' is the wordplay.
'start' suggests taking the first letters.
'by' means one lot of letters go next to another.
'a swimmer' becomes 'eel' (eel is a kind of aquatic vertebrate**).
The initial letter of 'false' is 'f'.
'f'+'eel'='FEEL'
'it's' is the link.
(Other definitions for feel that I've seen before include "Experience (an emotion)" , "Fondle" , "Experience, perceive" , "Consider" , "impression" .)