Unity subscription and Personal licenses work with any Unity Editor version, while legacy perpetual and pay-to-own licenses are version-locked but backward compatible. Perpetual licenses activate across their version and earlier ones, but pay-to-own licenses exclude LTS versions. Older licenses require purchasing a new subscription for newer versions. Older Unity versions are available via the download archive. Perpetual and pay-to-own licenses cannot be activated through the Hub.
Unity subscription licenses and Unity Personal licenses can be used on any version of the Unity Editor.
However, legacy perpetual* licenses and 'pay-to-own*' licenses are locked to a specific version of the Editor and are backward compatible.
For example, if you have a legacy Unity 4.X license, you can activate any version of Unity 4, or Unity 3. Perpetual Unity 5.X licenses can be activated in all versions of Unity 5, 4, and 3.
Pay-to-own* licenses are tied to the most recent, stable version of the Editor when the license was converted. These licenses are backward compatible on all prior versions except LTS (Long Term Support) versions of the Editor.
If you have an old license and want to activate on a newer version, you need to purchase a new subscription license.
To use an older version of Unity, you can download the version you are looking for from the download archive.
Note: Perpetual and pay-to-own licenses cannot be activated in the Hub.