Chaste priest leading strike within church (8)

I believe the answer is:

celibate

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'chaste' is the definition.
('celibate' can be similar in meaning to 'chaste')

'priest leading strike within church' is the wordplay.
'priest' becomes 'eli' (I've seen this before).
'leading strike' becomes 'bat' (I am not sure about the 'leading' bit.**).
'within' is an insertion indicator.
'church' becomes 'ce' (abbreviation for Church of England).
'eli'+'bat'='elibat'
'elibat' inserted within 'ce' is 'CELIBATE'.

Can you help me to learn more?

(Other definitions for celibate that I've seen before include "Belie act of being voluntarily chaste" , "Avowed bachelor" , "Not the marrying kind" , "Unmarried (person)" , "Living as a single person" .)

I've seen this clue in The Times.

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