Method of travel on rise? Don’t believe him! (4)
I believe the answer is:
liar
'don't believe him' is the definition.
(a liar should not be believed)
'method of travel on rise?' is the wordplay.
'method of travel' becomes 'rail'.
'on rise?' says the letters should be written backwards (in a down clue, letters go up).
'rail' back-to-front is 'LIAR'.
(Other definitions for liar that I've seen before include "Worse than a thief" , "One supplying pork pies" , "Perjurer" , "27 [DECEIVER]" , "Pinocchio, at times" .)