Is your problem that you have too many members, or that you think you don’t have enough money? Exclusive or not, tactful communication of any change is going to be important so that you don’t lose more members than you intended.
If you have the right number of members, you just don’t want any more, you might freeze the membership numbers and start taking a waiting list. You only add a new member when an existing member quits. You could also raise your prices for new memberships and keep the existing member rates the same. That keeps your “charter” members happy, and increases your revenue on new entrants.
If you have too many members now, raise the price for your existing members by 10% and then increase the joining fees and monthly rates for new members by 20%.
In your reason for changing pricing, you might focus on how long it’s been since the last time you raised rates and that your costs have increased. You might also mention that the membership increases will go towards something that benefits THEM (not just your profit) like new equipment or another staff person so that they have more individualized attention. Saying “Our gym is exclusive so I’m raising rates to scare people away,” could scare more people away than you intended.