The most common and most likely answer to this crossword clue is the 6 letter word EXETER
I've seen this crossword clue in The Daily Telegraph
E
X
E
T
E
R
More clues leading to the result EXETER
- For hearing, one that’s leaving city
- Heard someone leaving Devonian town
- City no longer safe when leader is deposed
- Henry’s uncle, divorcee, chopped up tree
- Former partner leads number wanting hotel in English city
- Diocese no longer safe when leader deposed
- Old film about revolutionary city
- Tree abandoned after heading off for Sex and the City
- Crown of every tenth tree blighted SW city
- English king returns, having captured French and English city
Buddy explains!

The straight part
We know that "diocese" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case diocese = exeter.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.