Leave nothing to be desired (7)

I believe the answer is:

satisfy

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'leave' is the definition.
The answer and definition can be both to do with fundamental existence as well as being verbs in their base form.
Maybe you can see a link between them that I don't see?

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

Can you help me to learn more?

(Other definitions for satisfy that I've seen before include "Meet the needs of (someone)" , "Satiate" , "Be good enough for" , "Meet, comply with" , "Meet the desires of" .)

I've seen this clue in The Globe and Mail.

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