Swimmer embarrassed by hairstyle (3,6)
I believe the answer is:
red mullet
'swimmer' is the definition.
(red mullet is a kind of fish)
'embarrassed by hairstyle' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'by' means one lot of letters go next to another.
'hairstyle' becomes 'mullet' (I've seen this before).
'red'+'mullet'='RED MULLET'
(Other definitions for red mullet that I've seen before include "Tasty swimmer" , "one's gathered in net" , "There's something fishy" , "Brightly coloured food fish" , "Fish -- dull meter (anag)" .)