A pup, as you may see, is not yet perfect (4)
I believe the answer is:
pupa
'not yet perfect' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'a pup as you may see' is the wordplay.
'a pup' anagrams to 'PUPA'.
Though, I'm unsure how the anagram is indicated.
'is' is the link.
Can you help me to learn more?
(Other definitions for pupa that I've seen before include "middle stage" , "Stage of an insect's development" , "not yet adult" , "creepy-crawly" , "Immature insect" .)