A common market for shorter pieces is anthologies.
You didn't give a length but "long poetry" is probably still not novel length.
Anthologies tend to have themes based on the subject of the work or the communities the author belongs to, or both. For example:
These are simply examples of anthologies I've read and liked. There are countless more. While science fiction and fantasy anthologies are common, there are plenty that don't have that theme. Most do not have requirements that the author belong to a particular community either. Though if you do belong to a particular community of any kind, do some searches. This includes living in a particular city.
Look at theme broadly. For example, if Goblin Market was just written and the author was trying to publish it, it could belong with stories of fantasy, fairy tale, horror, family ties, women, sisterly love, etc.
Consider graphic novel format.
Many anthologies are for graphic novel/comic book creators. You might consider partnering with an artist and submitting to anthologies using a creative illustrative style that doesn't have to look anything like most graphic novels.
If your poem is long enough (or if you have more than one that would work together), an illustrated book that is all your own might catch the eye of publishers more than a book of an epic poem.
I can imagine, for example, pages with long but narrow text down the middle and pictures and patterns in the very large margins.
Or pictures breaking up each stanza (or set of stanzas).
Or each page of text side by side with a full page illustration.
If you go this route, take your time finding the right artist and only get one, maybe two, sample pages to show publishers. Art is expensive!
Epic poetry isn't a big seller unless it's older works for school children, and even then... So the more you can position your work as part of other markets, the more successful you'll be. Good luck!