Keep going until finally dismissed (4,3)

I believe the answer is:

last out

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'keep going' is the definition.
(I've seen this before)

'finally dismissed' is the wordplay.
'finally' becomes 'last' (synonyms).
'dismissed' becomes 'out' (I've seen this before).
'last'+'out'='LAST OUT'

'until' is the link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for last out that I've seen before include "Endure" , "Keep on going" , "Manage to survive" , "one leaving after everyone else" , "when all the others have gone" .)

I've seen this clue in the Evening Standard.

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