Cool star caught English composer in a stew (6,3,5)

I believe the answer is:

chilli con carne

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'stew' is the definition.
(I have seen 'Spicy stew ' mean 'chilli con carne' so perhaps 'stew' could also mean 'chilli con carne')

'cool star caught english composer' is the wordplay.
'cool' becomes 'chill' (similar in meaning).
'star' becomes 'icon'.
'caught english' becomes 'c' (I can't justify this - if you can you should give a lot more credence to this answer).
'composer' becomes 'Arne' (Thomas Arne, composer of 'Rule Britannia').
'chill'+'icon'+'c'+'arne'='CHILLI CON CARNE'

'in a' is the link.

Can you help me to learn more?

(Other definitions for chilli con carne that I've seen before include "Spicy stew" , "meal" , "Spicy dish" , "fare" .)

I've seen this clue in The Times.

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