Greek letter making one's lip quiver (7)
I believe the answer is:
epsilon
'greek letter' is the definition.
(letter from the Greek alphabet)
'one's lip quiver' is the wordplay.
'quiver' indicates anagramming the letters (I've seen 'quivering' mean this (letters shake or quiver into a new order)).
'ones'+'lip'='oneslip'
'oneslip' is an anagram of 'EPSILON'.
'making' is the link.
(Other definitions for epsilon that I've seen before include "Greek letter E" , "character in Greece" , "Fifth letter of the Greek alphabet" , "Foreign character" , "Greek short E" .)