Person who doesn't want company car finally going after large one (5)
I believe the answer is:
loner
'person who doesn't want company' is the definition.
(a loner doesn't want people's company)
'car finally going after large one' is the wordplay.
'car' becomes 'RR' (Rolls Royce).
'finally going' means to remove the last letter (the final letter is removed).
'after' means one lot of letters go next to another.
'large' becomes 'L' (eg in clothes sizes).
'rr' with its last letter removed is 'r'.
'l'+'one'='lone'
'r' put after 'lone' is 'LONER'.
(Other definitions for loner that I've seen before include "Hermit" , "Enrol (anag)" , "Person shunning company" , "No mixer" , "Person who prefers his own company" .)