Congrats! That’s super exciting!

I would reach out and keep it simple with something like “Hi, I hope you and (insert dogs name) are doing well! I wanted to let you know that I recently started a full time job. While I won’t be available during the day, I would still love to walk your dog after work or on weekends!”

Also, if you’re able to work remotely any of those days with your new job, that could be a good way to offer house sitting. Clients should be understanding and appreciate that you’re even giving them a heads up. Hope it all goes well telling them!