Higher direct debit for very quiet milk supplier (5)

I believe the answer is:

udder

I'm a little stuck... Click here to teach me more about this clue!

'milk supplier' is the definition.
(I've seen this before)

I don't understand the remainder of the clue.

(Other definitions for udder that I've seen before include "Part of a cow" , "Steer with this" , "Bovine mammary gland" , "milk supplier" , "Cow's milk source" .)

I've seen this clue in The Telegraph.

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