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 an anagram.
'begun' with letters rearranged gives 'ungbe'.
'man' going around 'ungbe' is 'MUNG BEAN'.
'to eat' is the link.
I am not very happy about this link. Some or all of it may be part of 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" .)