Ballerina, say, getting cold in European river (6)
I believe the answer is:
dancer
'ballerina say' is the definition.
(ballerina is a kind of dancer)
'cold in european river' is the wordplay.
'cold' becomes 'c' (eg on taps).
'in' indicates putting letters inside.
'european' becomes 'dane' (someone from Denmark).
'river' becomes 'r' (abbreviation for river).
'c' put into 'dane' is 'dance'.
'dance'+'r'='DANCER'
'getting' acts as a link.
(Other definitions for dancer that I've seen before include "Terpsichorean" , "Eg, ballerina" , "One of Santa's reindeer" , "Mover to music" , "''I hope you have the feet of a ...'' (Charlie McGettigan)" .)