Heads off to terrible place (5)
I believe the answer is:
hades
'terrible place' is the definition.
'heads off' is the wordplay.
'off' is an anagram indicator.
'heads' with letters rearranged gives 'HADES'.
'to' acts as a link.
(Other definitions for hades that I've seen before include "It's hell in the Greek shade" , "A place of some darkness" , "Home of the souls of the dead" , "Classic hell in the shade" , "Hell of Greek myth" .)