Rig to relieve oil supplier (5,4)
I believe the answer is:
olive tree
'oil supplier' is the definition.
(as in olive oil)
'rig to relieve' is the wordplay.
'rig' is an anagram indicator (I've seen 'rigged' mean this).
'to'+'relieve'='torelieve'
'torelieve' with letters rearranged gives 'OLIVE TREE'.
(Other definitions for olive tree that I've seen before include "oil supplier" , "bearer of fruit" .)