Extradite soldiers at front of this carriage (10)
I believe the answer is:
deportment
'carriage' is the definition.
(I've seen this before)
'extradite soldiers at front of this' is the wordplay.
'extradite' becomes 'deport' (synonyms).
'soldiers' becomes 'men' (men can mean a group of soldiers).
'at front of' says to take the initial letters.
The first letter of 'this' is 't'.
'deport'+'men'+'t'='DEPORTMENT'
(Other definitions for deportment that I've seen before include "Behaviour - bearing" , "The way a person stands and walks" , "Conduct" , "Way of standing or walking" , "(Physical) bearing" .)