Measure Liberal and Labour backed in sport (8)
I believe the answer is:
football
'sport' is the definition.
(I know that football is a Olympic sport)
'measure liberal and labour backed' is the wordplay.
'measure' becomes 'foot' (foot is a kind of measure).
'liberal' becomes 'l' (abbreviation).
'and' is a charade indicator (letters next to each other).
'labour' becomes 'lab' (abbreviation).
'backed' says the letters should be written in reverse.
'lab' reversed gives 'bal'.
'l' put after 'bal' is 'ball'.
'foot'+'ball'='FOOTBALL'
'in' acts as a link.
(Other definitions for football that I've seen before include "Gambling on soccer results" , "Loft a lob badly in this game" , "The beautiful game, some say" , "Lob aloft (anag)" , "Ball game" .)