What are you nervous about?

You are relocating your business. No different than if you rented a storefront and are moving. Time to sign a new lease? Nope, I'm relocating. I've already signed another lease.

There is nothing you should be nervous or scared about. If you are truly a booth renter, your time there can end at anytime, and your current 'landlord' should know and expect that.

It's a business decision that really shouldn't involve your current landlord.

Just dont be a salon jumper like someone that ditches out on a rental house. Waiting untill the end of your current contract is fine. But if you are in the middle of a contract and you give notice the saturday before the monday you open your own shop and walk out -  that is totally wrong. Tell the salon owner at least a month ahead of time in you still are in contract and they should understand and be greatful for the heads up and can find another stylist to take your place. In this business you want to remain on friendly terms with as many stylist as you can. You never know when you may need them again.