The most common and most likely answer to this crossword clue is the 8 letter word COVENTRY
I've seen this crossword clue in The Times
C
O
V
E
N
T
R
Y
More clues leading to the result COVENTRY
- Witches struggle in a city
- Place heater in cold crack
- City witches go for
- Lines written by archdeacon in bed in cathedral city
- Some witches go in the city
- City which’s announced bid
- City firm opening on the outskirts of Rugby
- Witches go where outcasts are sent
- Group good at spelling test somewhere in the West Midlands
- Female gang to afflict Midlands city
Buddy explains!

The straight part
We know that "cathedral city" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cathedral city = coventry.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.