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Pester to rescind the dismissal (4,2)

Ross

I believe the answer is:

keep on

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'pester' is the definition.
Although both the answer and definition are verbs in their base form, I cannot see how they can define each other.

I cannot understand how the rest of the clue works.

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(Other definitions for keep on that I've seen before include "Continue, persevere" , "Continue; not dismiss" , "Continue; retain in service" .)

I've seen this clue in the Evening Standard.
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