Emergency transport’s appearance, a free ride (7)
I believe the answer is:
airlift
'emergency transport's' is the definition.
(transport used in an emergency)
'appearance a free ride' is the wordplay.
'appearance' becomes 'air' (both can mean an impression or character).
'a free ride' becomes 'lift' (as in a lift in someone's car).
'air'+'lift'='AIRLIFT'
(Other definitions for airlift that I've seen before include "Emergency supply by plane" , "emergency procedure" , "Transport in planes" , "Rescue using planes" , "Flying transportation" .)