I think you are trying to add a site to top sites. There is a known issue report at Brave GitHub and the fix is in Nightly 1.42.x. Until the fix reaches the stable version, there is a workaround. Posting the section of User Solutions: Brave Release 1.40.x that has links to the workarounds.
ISSUE: Cannot Add New Favorite Top Site
Source: Cannot add new favorite top site
Workarounds:
I can’t add favorite sites on my new tab - #5 by CerealLover
Cannot add new favorite top site - #11 by octo3010
Brave GitHub Issue Reports:
Fix layering issues with the NTP Add/Edit site dialog #13975
Fix: Implemented in Brave Nightly 1.42.x
Using Mouse Clicks when Adding or Editing Top Sites on NTP Closes the Dialogue Box #23689
Edit site is not working #23685
Related issue report also fixed by #13975