King's present unfeigned anger (12)
I believe the answer is:
frankincense
'king's present' is the definition.
(present given to the baby Jesus)
'unfeigned anger' is the wordplay.
'unfeigned' becomes 'frank' (frank can mean direct or genuine).
'anger' becomes 'incense' (incensing is a kind of angering).
'frank'+'incense'='FRANKINCENSE'
(Other definitions for frankincense that I've seen before include "Gift of one of the Magi" , "One of the gifts of the Magi" , "gift second to gold?" , "Christmas gift" , "One of the Magi's gifts" .)