Cheerful in putting a bit by (7)

I believe the answer is:

chipper

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'cheerful' is the definition.
('chipper' can be similar in meaning to 'cheerful')

'bit by' is the wordplay.
'bit' becomes 'chip' ('chip' can be a synonym of 'bit'**).
'by' becomes 'per'.
'chip'+'per'='CHIPPER'

'in putting a' acts as a link.
This may not be correct. Some or all of it may belong to 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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