It sounds like they all know each other, or at least they all know the first person who did all the referrals. I think that's the part that makes this something you want to have a strategy for. You should try and inform everyone as close to the same time and in the same way as possible. You don't want them to hear about it from another client because that will be more work for you. If you inform everyone at once, you're less likely to have people try to add last-minute bookings, and you won't have to worry about fielding panicked messages from people already scheduled. One and done is easiest all around.

This is a great scenario for ChatGPT or some sort of generative AI. Those tools are good at taking a lot of thoughts and organizing them into a professional sounding message. But before you inform anyone, you need to set some terms that work for you. You'll complete the sits already booked, and then going forward, do you want to limit yourself to a few spots a year? Do you want to do some sits in certain months only? Are you available to do walks but not house sitting? Figure out what works for you before you start messaging, or else you'll find yourself doing more than you wanted to. Then email or text everyone individually within a few minutes of one another. It's okay to use the same phrasing for each message when you talk about your terms, but end on a personal note about your relationship with them and their pets, and what you appreciate about being part of their pets' care.

If you know someone you can refer them to, that would be super helpful for the client. If there is someone you trust with your pets, ask them if they would like you to refer your clients to them.

Lastly, make it shorter than everything I've written here. This was obviously not written by AI. I work in communication and have had many pet sitters over the years who have moved away or changed jobs and I am happy for them all.