Are you struggling for bookings?
Essentially it's advertising, so if that week your apartment is empty anyway and you don't think you'll fill it, it could be worth it.
Make sure you agree certain parameters, e.g. 2 main posts, 3 stories, each tagging you Instagram page, plus a discount code when people booking using a specific code get 5% off their booking of a week or more with you.
Ensure sign-off from you about apartment content before posting - they could do a negative story about how unclean/ noisy/ smelly the apartment is if you don't (not saying it is, but who knows).
Alternatively, say you'll give them £100 discount for every person who books using the code they include on their post. So they pay up front for the week stay. Once followers have made bookings using the influencer's code you let them know and once that person has stayed and paid their bill you refund £100 to the influencer.
If they're confident their followers will book they'll be happy with this, if they're not confident why would you be?
Get everything agreed in writing if you do proceed.