Rage in peril, losing head (5)
I believe the answer is:
anger
'rage' is the definition.
(I've seen this before)
'peril losing head' is the wordplay.
'peril' becomes 'danger' (synonyms).
'losing head' means to remove the first letter.
'danger' with its initial letter taken off is 'ANGER'.
'in' is the link.
(Other definitions for anger that I've seen before include "Great annoyance" , "Hot displeasure; enrage" , "Extreme annoyance" , "Deadly sin" , "Irateness" .)