Move to cage island pet (6)
I believe the answer is:
budgie
'pet' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps you can see a link between them that I can't see?
'move to cage island' is the wordplay.
'move' becomes 'budge' (to budge is to move slightly).
'to cage' means one lot of letters goes inside another (inserted letters are locked up).
'island' becomes 'i' (geographical abbreviation).
'budge' going around 'i' is 'BUDGIE'.
Can you help me to learn more?
(Other definitions for budgie that I've seen before include "Abbreviated Australian cage-bird" , "Small colourful cage bird, in brief" , "Pet cage-bird from Australia" , "Small domestic parakeet" , "Popular cage-bird from Australia" .)