One's base: Roman building, all the rage (7)
I believe the answer is:
villain
'one's base' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'roman building all the rage' is the wordplay.
'roman building' becomes 'villa' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'all the rage' becomes 'in' (both can mean trendy).
'villa'+'in'='VILLAIN'
Can you help me to learn more?
(Other definitions for villain that I've seen before include "One played badly" , "Bad guy" , "Wrongdoer" , "Evil character" , "Principal fictional baddie" .)