Is the suspect, after drink knocked back, most aggressive? (8)

'most aggressive?' is the definition.
(pushy can mean aggressive or forceful)

'is the suspect after drink knocked back' is the wordplay.
'suspect' indicates anagramming the letters (a suspicious or unusual spelling).
'after' is a charade indicator (letters next to each other).
'drink' becomes 'sup' (to sup is to drink).
'knocked back' says the letters should be written backwards.
'sup' written backwards gives 'pus'.
'is'+'the'='isthe'
'isthe' with letters rearranged gives 'hiest'.
'hiest' put after 'pus' is 'PUSHIEST'.