Rest cut short? One expected rest (7)
I believe the answer is:
residue
'rest' is the definition.
(residue can mean the remains or rest of something)
'rest cut short? one expected' is the wordplay.
'cut short?' means to remove the last letter (I've seen 'cutting short' mean this).
'one' becomes 'i' (Roman numeral).
'expected' becomes 'due' (similar in meaning).
'rest' with its final letter taken off is 'res'.
'res'+'i'+'due'='RESIDUE'
(Other definitions for residue that I've seen before include "Remaining portion" , "What remains of something" , "It remains after other parts have been taken away" , "What is left, maybe dregs" , "Stuff left over" .)