Greek character and daughter back for a swim (3)
I believe the answer is:
dip
'a swim' is the definition.
(dip is a kind of swim)
'greek character and daughter back' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet**).
'and' means one lot of letters go next to another.
'daughter' becomes 'd'.
'back' says the letters should be written in reverse.
'pi'+'d'='pid'
'pid' backwards is 'DIP'.
'for' is the link.
(Other definitions for dip that I've seen before include "Sink; immerse" , "Informally a short bathe" , "may be lucky at the fete?" , "Lower into liquid" , "Slope downwards" .)