Make respectable-looking career, you heard, in oil company (5,2)
I believe the answer is:
brush up
'make respectable-looking' is the definition.
(brush up can mean to smarten something up)
'career you heard in oil company' is the wordplay.
'career' becomes 'rush' (career can mean to run or rush around).
'you heard' becomes 'U' (homophone of 'you').
'in' indicates putting letters inside.
'oil company' becomes 'BP' (British Petroleum).
'rush'+'u'='rushu'
'rushu' put into 'bp' is 'BRUSH-UP'.
(Other definitions for brush up that I've seen before include "Learn again" , "Renew one's knowledge of (a subject)" , "sort of refreshment?" , "Smarten, or revive knowledge of" , "Refresh one's knowledge" .)