Admit grift if heists regularly ignored (7)

I believe the answer is:

confess

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'admit' is the definition.
(confessing is a kind of admiting)

'grift if heists regularly ignored' is the wordplay.
'grift' becomes 'con' (I can't justify this - if you can you should give a lot more credence to this answer).
'regularly ignored' indicates alternate letters.
'if'+'heists'='ifheists'
The alternating letters of 'ifheists' are 'fess'.
'con'+'fess'='CONFESS'

Can you help me to learn more?

(Other definitions for confess that I've seen before include "Tell a priest one's sins" , "Admit (to crime)" , "Plead guilty (in order to receive absolution?)" , "Admit (to wrongdoing)" , "Concede" .)

I've seen this clue in The Independent.

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