Throws up three pieces of terrible shellfish (7)

I believe the answer is:

lobster

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'pieces of terrible shellfish' is the definition.
'lobster' can be an answer for 'shellfish' (lobster is a kind of shellfish). I am not sure about the 'pieces of terrible' bit.

'throws up three' is the wordplay.
'throws up' becomes 'lobs' (I've seen this before).
'three' becomes 'ter' (see Chambers).
'lobs'+'ter'='LOBSTER'

Can you help me to learn more?

(Other definitions for lobster that I've seen before include "Large marine decapod" , "Eight-legged shellfish, scarlet when boiled" , "Edible marine crustacean" , "Crustacean with pincer-like claws" , "could find this on the table" .)

I've seen this clue in The Sunday Times and The Times.

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