Small furry arboreal animal — us Poms (anag) (6)
I believe the answer is:
possum
(Other definitions for possum that I've seen before include "Play it to pretend to be asleep" , "Tree-dwelling Australasian marsupial" , "Marsupial - play it to feign sleep" , "Australian marsupial with dense fur and a long tail" , "Small furry Australian marsupial" .)