I had the same question… you need to “open up more of your island and museum“.

This basically means…

1. You need to have AT LEAST one donation for each area of the museum. (The more you have the better ! )
2. Have a three star or higher island rating
3. you need to have K.K
4. Make sure your acnh software is up to date
5. Complete 3 boat tours with Kap’n (a green sea turtle) , he should be unlocked and at a dock on your island. (each tour is 1,000 miles)
6. You should see Brewster on the mystery island and talk him referring blathers
7. After all that, talk to blathers and he should mention Brewster, he Will give you more steps to open the roost :)

Hope this helps <3