Now and again angered by daughter making demand (4)
I believe the answer is:
need
'demand' is the definition.
(synonyms)
'now and again angered by daughter' is the wordplay.
'now and again' indicates alternate letters (letters taken on a regular basis).
'by' says to put letters next to each other.
'daughter' becomes 'd'.
The alternating letters of 'angered' are 'nee'.
'nee'+'d'='NEED'
'making' acts as a link.
(Other definitions for need that I've seen before include "Necessity" , "Require; want" , "privation" , "Want - require(ment)" , "Rely on" .)