Carriage fetched, losing little time in the morning (8)
I believe the answer is:
brougham
'carriage' is the definition.
(brougham is a kind of carriage)
'fetched losing little time in the morning' is the wordplay.
'fetched' becomes 'brought' ('bring' can be a synonym of 'fetch').
'losing' indicates named letters should be taken away.
'little time' becomes 't' (abbreviation for time).
'in the morning' becomes 'am'.
'brought' with 't' removed is 'brough'.
'brough'+'am'='BROUGHAM'
(Other definitions for brougham that I've seen before include "Horse-drawn 19 down" , "Old carriage" , "Four-wheeled horse-drawn carriage" .)