Ive been a lifelong practitioner of Martial Arts since the early 60's. And the number one thing I can pass on to anyone who wants to stay fit is to maintain a strong core. All strength, balance, and recoiling movement comes from the core.
No matter how old you are , barring any physical barriers you can exercise your core. Yes theyre are other things that can be done, depending on physical form. But core work is very simple.