No - there is no such mechanism, and it is unlikely that one will be developed.
First a recap: HSTS allows a server to force clients to use HTTPS for a particular domain. Without HSTS, I can enable SSL on mydomain.com, but there is a risk that a attacker site could hijack a client (e.g. by DNS poisoning), and serve unauthorised plain-HTTP content for mydomain.com. Good user awareness has always been able prevent this (check the padlock), but the point of HSTS is that it gives protection even for novice users.
When it comes to TLS versions, as Terry Chia says, you can decide what versions you want your server to support. It's possible that a rogue server would try to impersonate your server, and use TLS versions that you have not enabled. But they would have to have a certificate for your domain - or some kind of vulnerability in an old version of TLS that they are exploiting. Considering that the published TLS protocol vulnerabilities are subtle issues that would not allow impersonation without a certificate, no-one is interested in developing such a system.