Forest's something eliminated by Brazilian president (4)
I believe the answer is:
bush
This clue is a triple definition!
'forest's' is the first definition.
(as in the Australian outback)
'something eliminated by brazilian' is the second definition.
(a Brazilian wax removes pubic hair)
'president' is the third definition.
(George H W Bush or George W Bush)
(Other definitions for bush that I've seen before include "Shrub; protective sleeve" , "Bull is often associated with this" , "Remote country" , "Shrub; metal lining" , "Low, woody plant" .)