Right to abandon run, embattled Biden initially not going, inflexible (9)

I believe the answer is:

unbending

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'inflexible' is the definition.
(synonyms)

'right to abandon run embattled' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to abandon' suggests deleting specific letters.
'embattled' becomes 'bending' (I can't justify this - if you can you should believe this answer much more).
'run' with 'r' taken away is 'un'.
'un'+'bending'='UNBENDING'

'biden initially not going' 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?

(Another definition for unbending that I've seen is " Rigid".)

I've seen this clue in The Times and The Sunday Times.

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