A membership is a client paying you every month whether or not they book. Done well it turns a lumpy book into predictable income, smooths the quiet months, and makes rebooking automatic. Done badly it is a discount you cannot escape.
It works where the service has a natural rhythm: a monthly maintenance appointment, a fortnightly fill, a treatment course. It does not work where visits are occasional or unpredictable — a membership for something people have three times a year is either bad value for them or a loss for you, and they will work out which.
Price it on attendance, not on the ideal. Some members will use every appointment and some will use half, and the ones who use every one are the ones who stay. Build the price so that a member who uses everything is still profitable, and treat the light users as the margin rather than as the plan.
Say what happens at the edges before anybody signs up: unused months, cancelling, whether appointments roll over, notice period, and whether the price is held if your prices rise. Every one of those is an argument if it is undefined, and all of them happen eventually.
Start small if you want to test it. One membership at one price, offered to your regulars, run for six months, then look at whether the people on it are coming more often than they did before. If they are not, it is a discount and nothing else.