Cheerful in putting a bit by (7)

I believe the answer is:

chipper

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'cheerful' is the definition.
(similar in meaning)

'bit by' is the wordplay.
'bit' becomes 'chip' (synonyms).
'by' becomes 'per' (I've seen this in another clue).
'chip'+'per'='CHIPPER'

'in putting a' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for chipper that I've seen before include "full of beans" , "Cheerful and lively (US)" , "Happy" , "Smartly-dressed" , "Smart" .)

I've seen this clue in the Evening Standard.

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