Fish in catch, one monster hauled up — snapper? (11)

'fish in catch' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps there's an association between them I don't understand?

'one monster hauled up snapper?' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'li' (I've seen this in other clues) and 'li' is found in the answer.
'monster' could be 'roc' (roc is a kind of monster) and 'roc' is located in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?