Heading away, perhaps June and I may be busy (2,3,2)
I believe the answer is:
on the go
'be busy' is the definition.
('on the go' can be similar in meaning to 'busy')
'heading away perhaps june and i' is the wordplay.
'heading away' means to remove the first letter.
'perhaps june' becomes 'month'.
'and' means one lot of letters go next to another.
'i' becomes 'ego' (I've seen this before).
'month' with its initial letter taken off is 'onth'.
'onth'+'ego'='ON THE GO'
'may' is the link.
(Other definitions for on the go that I've seen before include "Moving -- active" , "Keeping busy, not stopping" , "Very busy, in constant motion" , "ready to start monopoly?" , "Busy and active" .)