Anger shown by Pierre every now and then (3)
I believe the answer is:
ire
'anger' is the definition.
(ire is intense rage)
'pierre every now and then' is the wordplay.
'every now and then' indicates alternate letters (letters selected at regular intervals).
The alternate letters of 'pierre' are 'IRE'.
'shown by' acts as a link.
(Other definitions for ire that I've seen before include "heat" , "Displeasure" , "Anger among admirers" , "Anger, annoyance" , "'Anger, wrath (3)'" .)