With excellent degree, boy may finally become White House occupant (5,4)
I believe the answer is:
first lady
'white house occupant' is the definition.
(wife of a US president)
'with excellent degree boy may finally' is the wordplay.
'with' means one lot of letters go next to another.
'excellent degree' becomes 'first' (first-class degree).
'boy' becomes 'lad' (informal term for boy).
'finally' suggests the final letters.
The last letter of 'may' is 'y'.
'first' next to 'lad' is 'firstlad'.
'firstlad'+'y'='FIRST LADY'
'become' is the link.
(Other definitions for first lady that I've seen before include "Formerly, Jackie Kennedy for example" , "Michelle Obama, for example" , "Barbara Bush or Michelle Obama?" , "top partner" , "Twenty one [PRESIDENT]'s partner" .)