First you need to have the repository already downloaded and managed by HACS.
Once that is in place, find the card for the repository you want to enable beta releases for, and click the 3 dots in the bottom right corner of the card to bring up the repository menu. .
In that menu click on "Redownload" to bring up the Redownload dialog.
In the "Select version" dropdown, select the version you want to download and click the "Download" button in the bottom right of the dialog.
Not all repositories uses releases, it is up to the author of the repository to use that.