Overcomes bugs richer people finally zapped (4,3,6,2)

I believe the answer is:

gets the better of

'overcomes' is the definition.
(getting the better of is a kind of overcoming)

'bugs richer people finally zapped' is the wordplay.
'bugs' becomes 'gets'.
'richer people' becomes 'thebetteroff'.
'finally zapped' means to remove the last letter.
'thebetteroff' with its final letter taken off is 'thebetterof'.
'gets'+'thebetterof'='GETS THE BETTER OF'

I've seen this clue in The Times.

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