I like the idea of being outside and taking your client to a different location other than the gym–as it can help boost mood for you client. I do also agree with Sue and Karin. Although your client has clearance for participation in an exercise program, I would start with the client’s current fitness level. You also need to take into consideration any medications, and any other injuries or orthopedic issues she has before she starts her program.
A simple walking program to start may be suitable, and I would introduce some light resistance to her. You could take a light resistance band and use it to do exercises at the “corners” of the track. As your client gets stronger, you could also vary the walking pace for each lap (or half lap, etc..) you do.
Simply starting her program very slowly–and lending an ear if she needs to talk–is a great starting point.
Best to you and your client.