You need a health assessment for the pricey kinds of issues that any vet may see in their practice every year. If that makes sense - the things that aren’t that uncommon, even though they aren’t frequent. But are expensive.
Talk to your vet about what you have in mind. Such as, don’t care about minor unsoundness that won’t pain a companion horse. Do care about companion-horse maintenance-type issues, want a cost assessment of any found. “Lameness” matters, because a limpy horse is an ouchy horse. But there are some kinds of unsoundness that won’t be painful to a horse that is under no physical stress. Your vet will understand just what you need. 
I assume there is some pre-existing infirmity for the horse to be a companion horse, even if it is age. You can fill in any gaps in the PPE with some thought about your personal policies/guidelines for decisions on this horse’s future health issues. What I really mean is, decide what level of issue and spending are you willing to take on for this horse, should something come up. And when a sufficient loss of quality of life, with a treatment need that is beyond reasonable spending, means that it is time to let this horse gently pass on. It may be the greatest favor you could do for a horse whose only comfortable destiny is as a companion horse for some owner. With you, the horse will not be parked in pain in the pasture of an owner who is ignoring the inconvenience.
A friend recently took on a horse without knowing very much about it. Within the first couple of weeks the horse was diagnosed with uveitis, and it is proving to be a severe case. By now the friend has spent thousands on vet care and the prognosis is uncertain.
It’s unlikely something this bad will happen to your horse. But it’s wise to think things out when one isn’t in the pressure and emotion of major medical situation.
Congrats to you and your new companion horse on finding each other! 