Swimming style has fat go quickly (9)
I believe the answer is:
butterfly
'swimming style' is the definition.
(butterfly is a swimming stroke)
'fat go quickly' is the wordplay.
'fat' becomes 'butter' (I've seen this before).
'go quickly' becomes 'fly'.
'butter'+'fly'='BUTTERFLY'
'has' is the link.
(Other definitions for butterfly that I've seen before include "Peacock or red admiral, for example" , "Insect; flighty person" , "Winged insect and swimming stroke" , "Beautiful insect and swimming stroke" , "Swimming stroke - sort of net, kiss or screw" .)