Deranged senator gives great offence (7)
I believe the answer is:
treason
'great offence' is the definition.
'treason' can be an answer for 'offence' (I've seen this before). I'm unsure of the 'great' bit.
'deranged senator' is the wordplay.
'deranged' indicates an anagram.
'senator' is an anagram of 'TREASON'.
'gives' acts as a link.
Can you help me to learn more?
(Other definitions for treason that I've seen before include "Crime of disloyalty" , "LEse-majestE" , "Betrayal of the state" , "Betrayal of one's nation" , "Offence against state" .)