Downgrade woman getting to grips with vehicle test (6)
I believe the answer is:
demote
'downgrade' is the definition.
(I've seen this in another clue)
'woman getting to grips with vehicle test' is the wordplay.
'woman' becomes 'dee' (woman's name).
'getting to grips with' is an insertion indicator.
'vehicle test' becomes 'MOT' (MOT test).
'dee' going around 'mot' is 'DEMOTE'.
(Other definitions for demote that I've seen before include "Put down in rank" , "Relegate" , "Downgrade" , "Reduce in status" , "Move to lower status" .)