Divest driver who failed to finish without a record (7)
I believe the answer is:
deprive
'divest driver' is the definition.
'deprive' can be an answer for 'divest' (synonyms). I am not certain of the 'driver' bit.
'who failed to finish without a record' is the wordplay.
'who' becomes 'dr' (from TV series Doctor Who).
'failed to finish' becomes 'ive' (I can't explain this - if you can you should give a lot more credence to this answer).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'a record' becomes 'EP' (abbreviation for extended play record).
'dr'+'ive'='drive'
'drive' placed around 'ep' is 'DEPRIVE'.
Can you help me to learn more?
(Other definitions for deprive that I've seen before include "Debar from enjoyment" , "Withhold - divest" , "Deny (someone) use (of something)" , "Prevent (someone) from having" , "Dispossess (someone of something)" .)