Individual in pursuit of carriage (6)
I believe the answer is:
chaise
'carriage' is the definition.
(chaise is a kind of carriage)
'individual in pursuit' is the wordplay.
'individual' becomes 'i' (Roman numeral for one, ie individual).
'in' means one lot of letters goes inside another.
'pursuit' becomes 'chase' (synonyms).
'i' put into 'chase' is 'CHAISE'.
'of' is the link.
(Other definitions for chaise that I've seen before include "... longue, chair for reclining" , "Light open carriage" .)