Daughter called back, making peremptory request (6)
I believe the answer is:
demand
'peremptory request' is the definition.
(I've seen this before)
'daughter called back' is the wordplay.
'daughter' becomes 'd'.
'called' becomes 'named' ('name' can be a synonym of 'call').
'back' is a reversal indicator.
'd'+'named'='dnamed'
'dnamed' back-to-front is 'DEMAND'.
'making' is the link.
(Other definitions for demand that I've seen before include "Insistent request" , "Urgent or peremptory request" , "Stipulate" , "Request made emphatically as by right" , "Imperious request as for payment" .)