Carriage’s singular function on short trip east (8)
I believe the answer is:
stanhope
'carriage's' is the definition.
(I've seen this before)
'singular function on short trip east' is the wordplay.
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
'function' becomes 'tan' (tangent, mathematical function).
'on' says to put letters next to each other.
'short trip' becomes 'hop' (I have seen 'Short trip ' mean 'hop' so perhaps 'trip' could also mean 'hop'; 'short' indicates an abbreviation).
'east' becomes 'e' (synonyms).
's'+'tan'+'hop'+'e'='STANHOPE'
(Other definitions for stanhope that I've seen before include "Phaetons can be turned into a light open one-seater carriage" , "It may have only two wheels" , "carriage that has seat only for one" , "Light horse-drawn carriage; Nineteen across (anag.)" , "vehicle" .)