Led off after cake put in package (6)

I believe the answer is:

bundle

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'package' is the definition.
(I know that package can be written as bundle)

'led off after cake put in' is the wordplay.
'off' indicates an anagram.
'after cake' becomes 'bun' (bun is a type of cake. I am not sure about the 'after' bit.).
'put in' indicates putting letters inside.
'led' is an anagram of 'dle'.
'dle' placed around 'bun' is 'BUNDLE'.

Can you help me to learn more?

(Other definitions for bundle that I've seen before include "Swag for Australian" , "Things tied together" , "A third of a quarter" , "Loosely-tied collection" , "Loosely bound pile" .)

I've seen this clue in The Irish News.

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