Father carrying Henry to school in carriage (7)
I believe the answer is:
phaeton
'carriage' is the definition.
(thesaurus)
'father carrying henry to school' is the wordplay.
'father' becomes 'pa' (pa is a kind of father).
'carrying' means one lot of letters goes inside another.
'henry' becomes 'h' ('H' can be a synonym of 'henry').
'to school' becomes 'eton' (famous UK public school).
'pa' enclosing 'h' is 'pha'.
'pha'+'eton'='PHAETON'
'in' acts as a link.
(Other definitions for phaeton that I've seen before include "Coach" , "4-wheeled carriage" , "transport" .)