Crime that upsets senator (7)
I believe the answer is:
treason
'crime' is the definition.
(treason is a kind of crime)
'upsets senator' is the wordplay.
'upsets' indicates anagramming the letters.
'senator' anagrammed gives 'TREASON'.
'that' is the link.
(Other definitions for treason that I've seen before include "Deliberate act of betrayal" , "Serious crime" , "Stare on (anag.)" , "Act of betrayal of a government" , "Disloyalty (to one's country)" .)