The short answer is yes you can Airbnb a rental property... I do (I am in Australia).
As noted by @Marit-Anne0, it all comes down to your rental agreement currently in place. If it explicitly prohibits short term stays then I'd suggest you can't legally do it... local laws also come into effect.
I recommend most Hosts be open and honest with the Landlord so it's all above board... nothing changes from their perspective, you keep paying rent and actually have to take BETTER care of the place keeping it to a much cleaner standard for Guests etc.
Cheers,
Paul
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