Pays for conservative's false alibi (5,5)

I believe the answer is:

cover story

'false alibi' is the definition.
(false story providing an alibi)

'pays for conservative's' is the wordplay.
'pays for' becomes 'covers' (as in covering the cost of something).
'conservative' becomes 'tory' (informal term for a Conservative Party member).
'covers'+'tory'='COVER STORY'

I've seen this clue in The Times.

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