Paul came out with an admission of fault (3,5)
I believe the answer is:
mea culpa
'an admission of fault' is the definition.
(I've seen this before)
'paul came out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'paul'+'came'='paulcame'
'paulcame' is an anagram of 'MEA CULPA'.
'with' is the link.
(Other definitions for mea culpa that I've seen before include "I'm guilty (Latin)" , "Admission of fault" , "It's all my fault, said the old Romans" , "Admission of guilt by the old Romans" , "Acknowledgment of error or guilt" .)