Fastening a piece of wildlife film (9,4)

'fastening' is the definition.
(alligator clip is a kind of fastening)

'a piece of wildlife film' is the wordplay.
I cannot really understand how this works, but
'a' is found in the answer.
'piece' could be 'lip' (lip is a kind of piece) and 'lip' is present in the answer.
'of' could be 'o' and 'o' is found within the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?