First person ousted by more cheeky supporter taking cup (6)
I believe the answer is:
saucer
'supporter taking cup' is the definition.
(a saucer supports a teacup)
'first person ousted by more cheeky' is the wordplay.
'first person' becomes 'I' (first-person pronoun).
'ousted by' is a deletion indicator.
'more cheeky' becomes 'saucier' (saucy can mean cheeky or insolent).
'saucier' with 'i' taken out is 'SAUCER'.
(Other definitions for saucer that I've seen before include "Cup supporter" , "See 1" , "Piece of tableware, goes with cup" , "less than a plate?" , "Car use (anag)" .)