Follow on and acquit themselves really well (7)

I believe the answer is:

succeed

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'follow' is the definition.
(synonyms)

I can't explain the remainder of the clue.

(Other definitions for succeed that I've seen before include "Attain ambition" , "Take over a title from (someone)" , "Follow in order" , "Make good" , "Follow on - win" .)

I've seen this clue in the Evening Standard.

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