Absolutely demand extremes of loyalty (7)
I believe the answer is:
exactly
'absolutely' is the definition.
(thesaurus)
'demand extremes of loyalty' is the wordplay.
'demand' becomes 'exact' ('exact' can be a synonym of 'demand').
'extremes of' means to remove the middle letters.
'loyalty' with its centre taken out is 'ly'.
'exact'+'ly'='EXACTLY'
(Other definitions for exactly that I've seen before include "in nice way" , "Quite so" , "With precision" , "In precise terms" , "In every respect" .)