Swimmer finished last of lasagne - that's filling (9)

I believe the answer is:

fishpaste

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'filling' is the definition.
The answer and definition can be both things that one consumes for nourishment as well as being singular nouns.
Maybe you can see an association between them that I can't see?

'swimmer finished last of lasagne' is the wordplay.
'swimmer' becomes 'fish' (fish swim).
'finished' becomes 'past' (I've seen this in another clue).
'last of' says to take the final letters.
The final letter of 'lasagne' is 'e'.
'fish'+'past'+'e'='FISHPASTE'

'that's' is the link.

Can you help me to learn more?

I've seen this clue in The Daily Express.

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