Involve eastern doctor getting registered fuel (7)
I believe the answer is:
embroil
'involve' is the definition.
(I know that embroil is a more specific form of involve)
'eastern doctor getting registered fuel' is the wordplay.
'eastern' becomes 'e'.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'getting' says to put letters next to each other.
'registered' becomes 'R' (abbreviation, as in registered trademark).
'fuel' becomes 'oil' (oil is a type of fuel).
'e'+'mb'+'r'+'oil'='EMBROIL'
(Other definitions for embroil that I've seen before include "Involuntarily drag in" , "Tangle" , "Bring into confusion" , "In difficulties, involve" , "catch up" .)