Pianist father and daughter were backing runner (10)
I believe the answer is:
paderewski
'pianist' is the definition.
(Polish pianist Ignacy Paderewski)
'father and daughter were backing runner' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'and' is a charade indicator (letters next to each other).
'daughter' becomes 'd' (genealogical abbreviation).
'backing' says the letters should be written backwards.
'runner' becomes 'ski' (something which 'runs', ie moves quickly on snow).
'were' reversed gives 'erew'.
'pa'+'d'+'erew'+'ski'='PADEREWSKI'
(Other definitions for paderewski that I've seen before include "Former key player" , "Ignace Jan -, Polish pianist and statesman" , "Polish pianist and politician" , "Pianist who became prime minister of Poland" , "in Polish politics" .)