A simple yet useful tool to add depth to the players' characters. I always loved rolling for character backstory, piecing together what happened to them with each new roll, and I this submission provides that for characters in an ongoing campaign. I like how each result is followed up by questions to make you think about how to incorporate the result into a narrative. Good stuff. I can already see an otherwise good and by-the-book character rolling 5 every time and getting into trouble with authorities, and it's never their fault! That would impact how I roleplay that character for sure :D
My only note—a suggestion, really—is that getting multiple times a New Pet result would quickly get tiresome. I think a better option is to rewrite it into a New Friend option that mentions how this new friend can also be an animal. And getting a new friend as a result of rolling on this table would provide the Director with an excellent opportunity to use this new NPC for their nefarious purposes! Betrayal, kidnapping, leverage! Or just a natural source for providing new campaign-related information.