Have you edited the back matter in the 3rd book? Amazon will notify the people that purchased your book that there is an update.
They used to do that, years ago, but it doesn't happen now, unfortunately.
OP, it doesn't matter that your book is new or your series is older... the question is still that classic "how do i sell more books" question, no matter the details.
And the perennial answer to that question, besides mailing your list and hoping for help from Amazon: Paid advertising on book 1 will help you reach new readers, and may alert your previous readers about the new title at the same time. Bookbub featured deals are the best, and the rest is probably more viable than ever now that you have 4 books, with 3 to recoup a loss leader on the first.