Sure you can. BUT can't do it on a work visa so you'll need a training center.

You definitely can, it won't be on a work visa as they are not granted if you are older than 60 but there are definitely training centers out here that will hire you on a business or even tourist visa, especially considering that you are qualified, experienced and that schools in China are desperate for teachers (supply and demand, not enough supply)

You must be aware that working on any other visa than a work visa is illegal, as always in China the law is not always enforced but it has become increasingly strict in the past few years with police sometimes going to the training centers and checking foreigners' passports, if you are caught you can be fined, jailed and deported at your own expense, as well as blacklisted from returning to China for 5 years.

Apart from the obvious training centres who never bother with working visas in the first place, you might also be able to find something at a bigger college or university. Provided your employers have enough guan xi (relationships with government officials) anything is possible.

This having been said, it does seem that the authorities are cracking down on non-work visas though. So working in China without the correct visa has definitely gotten more risky.

The reason why is that once you are over 60 years of age, the mandatory health insurance can not cover you, so you can not work without it, and no work permit or work visa.

But I do know a case of an 87 years old retired teacher who has continued working legally by paying thru the nose for his own health insurance. It took a lot of paperwork to do it, but he got the work permit and work visa and he has been working as a teacher legally for many years.

I wouldn't hire you, you're too much of a liability.

Three foreign teachers in my small town over 60.  Two at a training centre and one at a middle school.  But all legal....to work in any capacity in Xinjiang one must be legal.