Here are some ways to discover poetry anthology publishers:
Research online: There are many websites and databases that list publishers and their areas of focus, such as Duotrope, Poets & Writers, and the Literary Marketplace.
Look at the acknowledgements page of poetry books: Many poets will thank the publisher in the acknowledgements section of their books, giving you a good idea of which publishers are active in the poetry community.
Check out poetry contests and prizes: Many publishers sponsor poetry contests and prizes, and the winning poets' work is often published by the sponsoring publisher.
Attend poetry events and readings: Many publishers have a presence at poetry events and readings, where you can meet editors and learn more about their publishing programs.
Ask other poets and writers for recommendations: Poets and writers often have a good sense of which publishers are reputable and which ones to avoid. They can also give you a sense of the submission process and what to expect.
Check out Literary agents: Many Literary agents work with poets, so it's a good idea to check out which agencies and agents are representing poetry, and which publishers they work with.
Visit bookstores and libraries: Bookstores and libraries often have sections dedicated to poetry, which can give you an idea of which publishers are producing poetry anthologies.
Look for poetry publishers in your area or region: Many publishers focus on poetry from a specific geographic area, such as small presses that focus on poets from a particular state or country.
Follow poetry publishers on social media: Many publishers now have social media accounts where they post about new releases and upcoming events.
Sign up for publishers' newsletters: Many publishers send out newsletters to their subscribers that include information on new releases, events, and submission guidelines.