A leading Catholic clergyman is precise (8)
I believe the answer is:
accurate
'precise' is the definition.
('accurate' can be similar in meaning to 'precise')
'a leading catholic clergyman' is the wordplay.
'leading' indicates taking the first letters.
'clergyman' becomes 'curate' (curate is a kind of clergyman**).
The first letter of 'catholic' is 'c'.
'a'+'c'+'curate'='ACCURATE'
'is' acts as a link.
(Other definitions for accurate that I've seen before include "Precise, correct" , "telling it like it is" , "True!" , "Spot on" , "Absolutely correct" .)