Crossword Genius

Rear half of studio, once, base for bishop's office (7)

Ross

I believe the answer is:

diocese

'bishop's office' is the definition.
(a diocese is the area a bishop is responsible for)

I cannot understand how the remainder of the clue works.

(Other definitions for diocese that I've seen before include "Bishop's see" , "Ecclesiastical see" , "District under a bishop's authority" , "I see cod (anag)" , "District under care of bishop" .)

I've seen this clue in The Times.
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