Old player in cricket team backed by leader of Conservatives — would one often open for Churchill? (5,3)
I believe the answer is:
'would one often open for churchill?' is the definition.
(Winston Churchill smoked cigars)
'old player in cricket team backed' is the wordplay.
'old player' becomes 'Garbo' (actress Greta Garbo, c905-c990).
'in' indicates putting letters inside.
'cricket' becomes 'c' (this could be a standard abbreviation I've not previously seen).
'team' becomes 'XI' (a football team, from Roman numerals for cc).
'backed' is a reversal indicator.
'xi' backwards is 'ix'.
'garbo' placed inside 'cix' is 'CIGAR BOX'.
'by leader of conservatives' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.