When I hit extensions in your browser and search for Alby there is nothing. No results at all.
Brave is based on Chromium. So you can just download Alby from here: https://chrome.google.com/webstore/detail/alby-bitcoin-lightning-wa/iokeahhehimjnekafflcihljlcjccdbe
If you see any error message. Please send a screenshot to support@getalby.com and I'll help you there.
Discussion
Did you install Alby from the link above in the Brave browser? It could be that it is hidden and you have to pin it to the browser bar. Click on the puzzle piece in the top right of your browser and select the pin next to the Alby icon.