Letter from Greece upset soldier's mum (5)
I believe the answer is:
sigma
'letter from greece' is the definition.
(letter from the Greek alphabet)
'upset soldier's mum' is the wordplay.
'upset' says the letters should be written in reverse.
'soldier's' becomes 'GI's' (term for US soldier).
'mum' becomes 'ma' (both can mean mother).
'gis' reversed gives 'sig'.
'sig'+'ma'='SIGMA'
(Other definitions for sigma that I've seen before include "Letter from Greece" , "letter to Greeks" , "Allowing no relaxation" , "character abroad" , "Greek character" .)