Walk wearily heading away for slope (4)
I believe the answer is:
ramp
'for slope' is the definition.
(I've seen this before)
'walk wearily heading away' is the wordplay.
'walk wearily' becomes 'tramp' (I've seen this before).
'heading away' means to remove the first letter (the word's 'head' is removed).
'tramp' with its first letter removed is 'RAMP'.
(Other definitions for ramp that I've seen before include "what could be criminal offence" , "Level-connecting slope" , "Sloping surface; swindle" , "Sloping platform" , "aircraft steps?" .)