Eats after almost the right warnings (7)
I believe the answer is:
threats
'warnings' is the definition.
(I know this)
'eats after almost the right' is the wordplay.
'after' means one lot of letters go next to another.
'almost' means to remove the last letter (most of the word but not all of it).
'right' becomes 'r' (common abbreviation).
'the' with its final letter taken away is 'th'.
'th'+'r'='thr'
'eats' after 'thr' is 'THREATS'.
(Other definitions for threats that I've seen before include "Terrifying demands" , "Expressions of intention to harm" , "Statements of intentions to harm" , "Shatter (anag) - menaces" , "Menacing statements" .)