Periodically nutmegged, receiving supporter's anger (7)
I believe the answer is:
umbrage
'anger' is the definition.
(umbrage is a kind of anger)
'periodically nutmegged receiving supporter's' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'receiving' means one lot of letters goes inside another.
'supporter' becomes 'bra' (I've seen this before).
The alternating letters of 'nutmegged' are 'umge'.
'umge' enclosing 'bra' is 'UMBRAGE'.
(Other definitions for umbrage that I've seen before include "Take this to show offence" , "Offence, annoyance" , "Resentment, offence" , "Feeling of offence" , "Displeasure" .)