Minor hearing about sex in Rome (7)
I believe the answer is:
trivial
'minor' is the definition.
(thesaurus)
'hearing about sex in rome' is the wordplay.
'hearing' becomes 'trial' (I've seen this before).
'about' is an insertion indicator.
'sex in rome' becomes 'vi' (I can't explain this - if you can you should give a lot more credence to this answer).
'trial' going around 'vi' is 'TRIVIAL'.
Can you help me to learn more?
(Other definitions for trivial that I've seen before include "Quite unimportant and paltry" , "Of little substance or significance" , "Meaningless" , "not significant" , "Of little importance" .)