Clean out the self-starter for a cash incentive (5)

I believe the answer is:

purse

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'cash incentive' is the definition.
'purse' can be an answer for 'cash' (thesaurus). I am unsure of the 'incentive' bit.

'clean out the self-starter' is the wordplay.
'clean' becomes 'pure' (similar in meaning).
'out' is an insertion indicator.
'starter' indicates taking the first letters.
The initial letter of 'self' is 's'.
'pure' placed around 's' is 'PURSE'.

'for a' acts as a link.

Can you help me to learn more?

(Other definitions for purse that I've seen before include "Prize in boxing" , "Compress (lips)" , "Knit" , "bag for loose change" , "Means < to close" .)

I've seen this clue in the Evening Standard.

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