Food-store feeds apple skin to small penguin (6)

'small penguin' is the definition.
(I've seen this in another clue)

'food-store feeds apple skin' is the wordplay.
'food store' becomes 'deli' (I've seen this before).
'feeds' means one lot of letters goes inside another.
'skin' suggests removing the centre (only the skin or outside of the word is used).
'apple' with its middle removed is 'ae'.
'deli' put into 'ae' is 'ADELIE'.

'to' is the link.