Exploit a vet's elephant for environmental slogan (4,3,6)

I believe the answer is:

save the planet

I'm a little stuck... Click here to teach me more about this clue!

'environmental slogan' is the definition.
I know nothing about this answer so I can't tell whether this works.

'exploit a vet's elephant' is the wordplay.
'exploit' is an anagram indicator (I've seen 'exploited' mean this).
'a'+'vets'+'elephant'='avetselephant'
'avetselephant' with letters rearranged gives 'SAVE THE PLANET'.

'for' is the link.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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