Vet disheartened, seeing this little beast (6)
I believe the answer is:
insect
'this little beast' is the definition.
'insect' can be an answer for 'beast' (insect is a kind of beast). I'm not sure about the 'this little' bit.
'vet disheartened' is the wordplay.
'vet' becomes 'inspect' (inspect can mean to vet or check).
'disheartened' means to remove the middle letters (the middle or heart is removed).
'inspect' with its middle removed is 'INSECT'.
'seeing' is the link.
Can you help me to learn more?
(Other definitions for insect that I've seen before include "A fly, for instance" , "Bee or beetle, for example" , "Small creature with six legs and no backbone" , "Possibly fly" , "Bug" .)