Pricing is the single most leveraged decision an independent PMU artist makes, and it is the one most artists are afraid to touch. Here is the protocol I use, refined over twenty years and four price changes of my own.
Step one: change the calendar before the price
Before you raise prices, change what you offer. Add a new service, remove an old one, restructure your packages. The price change then attaches to a real change in what the client is buying, not just inflation in your opinion of yourself.
Step two: tell existing clients first, in writing
The new price applies to new bookings. Existing clients get written notice at least six weeks before their next regular appointment, with the option to book once more at the old rate. This turns a price increase into a grace period. Almost nobody cancels.
Step three: do not apologize
Do not use the words due to, unfortunately, or as you know. State the new price as a fact about the present, the way a restaurant states the menu. The client decides.
Step four: have something to show
If a client asks why, the answer is a service change, a new technique, a certification, a year of experience. Prepare it. Say it once and then move on.
Prices are not a measure of your worth as a human. They are a measure of how much of your time and skill someone else gets. Decide what that's worth and write it down.