Steps down - or steps up again! (7)
I believe the answer is:
resigns
'steps down' is the definition.
(resigning is a kind of stepping down)
'steps up again' is the wordplay.
I cannot really see how this works, but
'again' could be 're' (prefix meaning 'again') and 're' is found in the answer.
The remaining letters 'signs' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'or' acts as a link.
Can you help me to learn more?
(Other definitions for resigns that I've seen before include "abdicates" , "Gives up (a post)" , "Leaves job voluntarily" , "does the honourable thing" .)