Shame there's no time for foreign character (5)
I believe the answer is:
sigma
'foreign character' is the definition.
(Greek letter)
'shame there's no time' is the wordplay.
'shame' becomes 'stigma' (stigma can mean shame or disgrace).
'there's no' indicates named letters should be taken away.
'time' becomes 't' (abbreviation).
'stigma' with 't' taken out is 'SIGMA'.
'for' is the link.
(Other definitions for sigma that I've seen before include "The 18th letter of the Greek alphabet" , "Greek letter signifying sum in maths" , "Foreign character" , "Letter from Athens" , "Athenian character" .)