The most common and most likely answer to this crossword clue is the 8 letter word BROMANCE
I've seen this crossword clue in The Guardian
B
R
O
M
A
N
C
E
More clues leading to the result BROMANCE
- Bishop with Catholic church in which men connect
- Caesar, perhaps, in his day and age had one with Antony …
- British country church, in which men bond
- Buddies have this non-British party in British city
- Live to embrace Italian chap, primarily – that’s love between men
- British novel about the end of one chap’s relationship with another
- Close relationship with British and Italian church
- Country separating couple, not wanting a loving relationship between men
- Platonic attachment of Nero, say, in pre-Christian time
- All-male relationship as couple heartlessly broken up by sultanate
Buddy explains!

The straight part
We know that "had one with Antony" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case had one with antony = bromance.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.
What does BROMANCE mean?
BROMANCE noun- A close but non-sexual relationship between men.