Goes to the gallows, not the first time, in dread (5)
I believe the answer is:
angst
'dread' is the definition.
(I know that dread can be written as angst)
'goes to the gallows not the first time' is the wordplay.
'goes to the gallows' becomes 'hangs' (hangs from a gallows).
'not the first' means to remove the first letter.
'time' becomes 't' (abbreviation).
'hangs' with its initial letter removed is 'angs'.
'angs'+'t'='ANGST'
'in' is the link.
(Other definitions for angst that I've seen before include "Nagging worry" , "Philosophical unease" , "Acute anxiety about oneself" , "Acute but unspecified feeling of worry" , "Strong feeling of anxiety/dread" .)