Get round to eating bananas with sweetheart (9)
I believe the answer is:
negotiate
'get round' is the definition.
'to eating bananas with sweetheart' is the wordplay.
'bananas with' is an anagram indicator (informal term for mad).
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'to'+'eating'='toeating'
'toeating' anagrammed with 'e' makes 'NEGOTIATE'.
(Other definitions for negotiate that I've seen before include "Discuss the terms of an arrangement" , "Deal, bargain" , "treat! Yes!" , "Bring about by mutual agreement" , "I get a note (anag) - bargain" .)