Fellow having unexpectedly begun to eat vegetable (4,4)
I believe the answer is:
mung bean
'vegetable' is the definition.
(I have seen 'Tropical vegetable ' mean 'mung bean' so perhaps 'vegetable' could also mean 'mung bean')
'fellow having unexpectedly begun' is the wordplay.
'fellow' becomes 'man' (fellow can mean a man).
'having' is an insertion indicator.
'unexpectedly' indicates anagramming the letters.
'begun' with letters rearranged gives 'ungbe'.
'man' placed around 'ungbe' is 'MUNG BEAN'.
'to eat' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for mung bean that I've seen before include "Tropical vegetable" , "Edible seed" .)