This little fellow is a cross one when deprived of pie (5)
I believe the answer is:
pixie
'this little fellow' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe there's an association between them I don't understand?
'cross one when deprived of pie' is the wordplay.
I cannot really understand how this works, but
'cross' could be 'x' (an X is a cross) and 'x' is found in the answer.
'one' could be 'i' (Roman numeral) and 'i' is found in the answer.
The remaining letters 'pie' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'is a' acts as a link.
Can you help me to learn more?
(Other definitions for pixie that I've seen before include "Sprite" , "Elf, imp" , "Mischievous fairy" , "Creature like fairy or elf" , "Little person" .)