Hurry up and get big diaper on son (4,2,6)

I believe the answer is:

make it snappy

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'hurry up' is the definition.
(phrase used to tell someone to hurry up)

'big diaper on son' is the wordplay.
'big' becomes 'makeit' (I can't justify this - if you can you should believe this answer much more).
'diaper' becomes 'nappy' (synonyms).
'on' is a charade indicator (letters next to each other).
'son' becomes 's' (genealogical abbreviation for son).
'nappy' after 's' is 'snappy'.
'makeit'+'snappy'='MAKE IT SNAPPY'

'and get' is the link.

Can you help me to learn more?

(Other definitions for make it snappy that I've seen before include "Get a move on!" , "To annoy a dog, perhaps" , "Hurry up! (slang)" , "do it quickly" , "step on it" .)

I've seen this clue in The Independent.

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