Cathedral cleric, second one ousted (7)

I believe the answer is:

minster

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'cathedral' is the definition.
(minster is a kind of cathedral)

I don't understand the remainder of the clue.

(Other definitions for minster that I've seen before include "Large church (or cathedral at York)" , "Clergyman" , "Abbey or priory church" , "Old monastic cathedral, such as York's" , "Large church (eg, York)" .)

I've seen this clue in The Sun.

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