First you need to make sure the clubs you will be approaching actually allow independent trainers to come in and use their space. Some questions you will need to ask are regarding:
-the fees/rent you will need to pay (either monthly or per session)
-the type of liability insurance they require independent contractors to have
-times/hours that independent trainers are allowed into their space (if applicable)
-the number of clients you are allowed to train at the same time
-the type of equipment you are allowed to bring in their space in case you have some that you would like to use
-some gyms may supply you with clients of their own, so you need to know what their policy is in that case
-if they ask you to sign a non-compete agreement make sure to take a close look at it and see if that is something that you agree with
-make sure they have the correct information regarding your tax information
I hope this helps.
I’d like to add that you need to inquire whether you can bring in clients who are not members of the club, and if yes, what the policy is there.
I was once an independent trainer at a gym, and when all my clients became members there, I had an even better relationship with the gym because they saw my added value to their club without having to provide me with anything at all.