After you have installed EndNote 21, you may see when you open a library:
Versions of EndNote from EndNote X9.3.1 onwards differ from earlier versions in that they are not backwards compatible. A library created using EndNote X9.3.1 or a library converted to EndNote X9.3.1 cannot be used by an earlier version. They explain:
EndNote X9.3/EndNote 20/EndNote 21: Library Conversion and Backward Compatibility
EndNote X9.3 introduced a new database engine to EndNote. EndNote X9.3 and later libraries will not be backwardly compatible with older versions of EndNote. If you work in an environment with multiple versions of EndNote, you can convert your libraries to the new database engine using the instructions below.
To use libraries created with EndNote X9.2 and earlier, convert the library through EndNote X9.3 or later. To do this, in EndNote X9.3 or later select File / Open / Open Library...and select the old EndNote library file you wish to convert. EndNote X9.3 or later will create a new library and leave the original library unchanged.
On a PC, if you still have Endnote X9.2 (or even X8) installed, you can continue to use it, although there will be no updates.
There are potential problems. If you want to send a library (a compressed library) that used Endnote X9.3.1 to someone who has Endnote X9.2, they will be unable to use it. (They suggest synchronize with the online EndNote as a way to share.)
If it doesn't matter, Endnote X9.3.1 converted libraries should work for you without trouble.