Collier goes to Virginia to see a goddess (7)
I believe the answer is:
'a goddess' is the definition.
(I've seen this before)
'collier goes to virginia' is the wordplay.
'collier' becomes 'miner' (I've seen this before).
'goes to' means one lot of letters go next to another.
'virginia' becomes 'va' (US state abbreviation).
'to see' acts as a link.
(Other definitions for minerva that I've seen before include "Roman counterpart of Athene" , "wise goddess" , "Divine female" , "embodiment of wisdom" , "Roman goddess of learning" .)