I would recommend running a full blood panel and urinalysis to help determine if there are any underlying health problems and to establish a baseline for future tests.
One thing that you may need to address is dental care. Many senior pets will require a dental cleaning and possibly extractions. Infected gums or bad teeth can introduce bacteria into the bloodstream which can affect internal organs such as kidneys. It's good to take care of problems asap.
Yes! Great advice there, and I definitely second Yodel's advice.
Bloodwork and a good dental is definitely in order.
Every single one of my guys, even some of my young ones, had bloodwork and a dental done when they came into my home. The only exception was Jake, who had bloodwork but no dental because of his very bad heart.
I actually did the dental on everybody when they were each getting spayed/neutered, so it could all be done in one shot. Blue, Bo, Gracie, Mattie, you name it, all had bad teeth and needed some extractions and a good dental cleaning. Blue had major teeth issues, and Gracie's were just pitiful. Callie, who came to me at 5 years old, also had serious teeth issues (but they all came as puppymill breeders, and I think it was their bad breeding that caused their teeth to be so bad).
Bloodwork is another really good idea. Blue had bloodwork and had some protein and billirubin in his urine, which indicated that we just needed to keep an eye on his renal organs. So far, so good though. When we first got Jake, bloodwork showed us he had some heart issues besides the obvious heart murmur that could be heard. So we did x-rays and an ECG and confirmed mitral valve prolapse, congestive heart failure, and a enlarged heart.
But here's the thing, I don't want the thought of having to do bloodwork, or doing extra care, to scare you off from a senior. Seniors are such amazing dogs to have, and are often overlooked by people wanting that younger dog, or cute puppy. A lot of people don't want the seniors because of their older age, and some of the problems that come along with them. And it's sad, because they make some of the most amazing pets.
So count yourself blessed and lucky to be welcoming a senior into your home, you'll get tons of love in return!