Not all state emissaries are seen in large numbers (4)

I believe the answer is:

teem

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'not all state emissaries are seen in large numbers' is the definition.
I can't tell whether this defines the answer.

'not all state emissaries are' is the wordplay.
'not all' says the answer is hidden in the clue.
'TEEM' is hidden in the letters of 'state emissaries are'.

Can you help me to learn more?

(Other definitions for teem that I've seen before include "Flow copiously" , "Rain buckets" , "Abound - pour" , "Move in large numbers" , "Rain cats and dogs" .)

I've seen this clue in the Evening Standard.

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