Affair with female was on report (7)
I believe the answer is:
shebang
'affair' is the definition.
('shebang' can informally refer to a matter)
'female was on report' is the wordplay.
I cannot really see how this works, but
'female' could be 'she' ('she' refers to a woman) and 'she' is found in the answer.
'report' could be 'bang' (report can mean a loud noise) and 'bang' is found within the answer.
No letters remain.
This explanation may well be incorrect...
'with' acts as a link.
Can you help me to learn more?
(Other definitions for shebang that I've seen before include "affair in America" , "Matter" , "(Whole) kit and caboodle" , "circumstances" , "Lot" .)