Moving right up the rat menace (6)
I believe the answer is:
threat
'menace' is the definition.
('threat' can be a synonym of 'menace')
'moving right up the rat' is the wordplay.
'the rat' anagrams to 'THREAT'.
But, I am not clear how this is indicated.
(Other definitions for threat that I've seen before include "Declaration of intention to harm another" , "Menace of impending evil" , "Aggressive declaration" , "Hatter (anag)" , "Statement of intention to harm" .)