Refined grade 'A' ore almost becomes a driving passion (4,4)
I believe the answer is:
road rage
'a driving passion' is the definition.
(passionate anger when driving)
'refined grade a ore almost' is the wordplay.
'refined' is an anagram indicator.
'almost' means to remove the last letter (most of the word but not all of it).
'grade'+'a'+'ore'='gradeaore'
'gradeaore' with its final letter taken off is 'gradeaor'.
'gradeaor' with letters rearranged gives 'ROAD RAGE'.
'becomes' is the link.
(Other definitions for road rage that I've seen before include "Uncontrollable temper experienced by some drivers" , "Motorway ire" , "making of a scene for travellers?" , "Motorway madness?" , "Driver's violent anger" .)