Following crafty veteran, essentially (5)

I believe the answer is:

after

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'following' is the definition.
(following can mean after or as a result of)

'crafty veteran essentially' is the wordplay.
'crafty' becomes 'af' (I can't justify this - if you can you should believe this answer much more).
'essentially' says to take the centre.
The middle letters of 'veteran' are 'ter'.
'af'+'ter'='AFTER'

Can you help me to learn more?

(Other definitions for after that I've seen before include "Coming later in time" , "Following - behind" , "Chasing" , "In honour of" , "Subsequently" .)

I've seen this clue in The Irish Times.

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