Reportedly cold, long for one to supply wood (5,4)
I believe the answer is:
chile pine
'one to supply wood' is the definition.
(wood might come from a chile pine)
'reportedly cold long' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'cold' becomes 'chilly' (I've seen this before).
'long' becomes 'pine' (to pine for someone is to long for them).
'chilly' is a homophone of 'chile'.
'chile'+'pine'='CHILE-PINE'
'for' is the link.
(Other definitions for chile pine that I've seen before include "One [TYPE OF TREE]" , "wood from South America" , "Monkey puzzle tree - Araucaria" , "Leaving body" .)