Could do, you say, with a little (4)

I believe the answer is:

mite

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'a little' is the definition.
(thesaurus)

I don't understand how the rest of the clue works.

(Other definitions for mite that I've seen before include "Tiny creature found in food" , "The widow's small offering" , "The widow's contribution, just in time" , "Minute arachnid" , "The widow's small donation" .)

I've seen this clue in the Evening Standard.

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