Father fast making highest church office (6)

I believe the answer is:

papacy

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'church office' is the definition.
(I've seen this before)

'father fast' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'fast' becomes 'pacy' (I've seen this in other clues).
'pa'+'pacy'='PAPACY'

'making highest' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for papacy that I've seen before include "Pope's office" , "high church job" , "Vatican leader's office" , "form of Fatherhood?" , "ecclesiastical office" .)

I've seen this clue in The Times.

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