Throttling killer disposing of line is not so normal (8)
I believe the answer is:
stranger
'not so normal' is the definition.
(more strange ie less normal)
'throttling killer disposing of line' is the wordplay.
'throttling killer' becomes 'strangler' (someone who kills by strangling).
'disposing of' suggests deleting specific letters.
'line' becomes 'l' (used when specifying particular lines from a poem).
'strangler' with 'l' taken out is 'STRANGER'.
'is' is the link.
(Other definitions for stranger that I've seen before include "'Fact is ........ than fiction'" , "Unfamiliar person" , "One who is little known" , "More rum" , "More odd or weird" .)