Almost suggest poem and go off (7)
I believe the answer is:
implode
'go off' is the definition.
('implode' can be a synonym of 'go off')
'almost suggest poem' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'suggest' becomes 'imply' (implying is a kind of suggesting).
'poem' becomes 'ode' (ode is a kind of poem).
'imply' with its final letter taken away is 'impl'.
'impl'+'ode'='IMPLODE'
'and' acts as a link.
(Other definitions for implode that I've seen before include "Collapse suddenly inwards" , "Burst inward" , "Cause to burst inwards" , "Violently collapse inwards" .)