Even the finest can be overrun! (6)

I believe the answer is:

infest

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'overrun' is the definition.
('infest' can be a synonym of 'overrun')

'even the finest can' is the wordplay.
'finest' can be anagrammed to 'INFEST'.
However, I'm not sure how the anagram is indicated.

'be' acts as a link.

Can you help me to learn more?

(Other definitions for infest that I've seen before include "Hostile once" , "Feints to be numerous and troublesome" , "Annoyingly swarm through" , "(E.g. vermin) abound in" , "Finest (anag)" .)

I've seen this clue in the Evening Standard.

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