Carriage papa originally had at college (7)
I believe the answer is:
phaeton
'carriage' is the definition.
(type of horse-drawn carriage)
'papa originally had at college' is the wordplay.
'papa' becomes 'P' (phonetic alphabet: alpha, bravo, charlie etc.).
'originally' suggests taking the first letters.
'college' becomes 'eton' (Eton College, English private school).
The first letters of 'had at' is 'ha'.
'p'+'ha'+'eton'='PHAETON'
(Other definitions for phaeton that I've seen before include "Coach" , "transport" , "4-wheeled carriage" .)