… and not half common! (3)

I believe the answer is:

nor

'and not' is the definition.
(I've seen this before)

'half common' is the wordplay.
'half' indicates taking half.
'common' becomes 'normal' (I've seen this before).
'normal' halved is 'NOR'.

(Other definitions for nor that I've seen before include "Link word" , "logic circuit" , "It's also not" , "Neither pairing" , "And not; Norman (abbr.)" .)

I've seen this clue in The Times.

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