Strength of character essential to integrity (4)

I believe the answer is:

grit

'strength of character' is the definition.
(I've seen this in another clue)

'essential to integrity' is the wordplay.
'essential to' indicates a hidden word (I've seen this in other clues).
'GRIT' can be found hidden inside 'integrity'.

(Other definitions for grit that I've seen before include "Bottle" , "Fortitude" , "Particles of stone/sand" , "True determination?" , "Courage - clench - small particle of stone" .)

I've seen this clue in The Independent.

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