With each major version of ArcGIS, ESRI make changes to the database schema. They make sure that newer versions of ArcMap can read older versions of the database schema. But of course its not possible for older versions of ArcMap to read databases created with a newer schema, as that schema did not exist when that version of ArcMap was published.
It is possible to upgrade an enterprise geodatabase to the newer schema, but it cannot be downgraded to an older schema.
If you need to access the database from different versions of ArcMap, then you need to create the database using the oldest version that you want to support. (And don't upgrade the database schema version until all of your users have upgraded ArcMap.)
So, you will need to either:
- Upgrade all users to the new version of ArcMap
- Re-create the database using the old version of ArcGIS, migrate all the data across and delete (or disable) the other database
- Stop supporting the users who run old versions of ArcMap