Most popular music streaming services such as Spotify, Pandora, Apple Music, and TIDAL already pay streaming royalties out to music publishers. Therefore, you don’t need to obtain a streaming license for distribution on those platforms. However, certain music hosting sites such as Bandcamp do not have license agreements in place with music publishers and therefore would require you to obtain a streaming license if you intend to host your music via their service.
In the case of YouTube, many music publishers have entered into license agreements allowing the use of their songs in exchange for a percentage of Ad revenue. You can search for the song you want to post to see if use of the song is permitted. If not, you will most likely need to contact the publisher(s) directly to inquire about posting your cover song on YouTube.
Aside from streaming uses, if you intend to distribute a digital download of your cover song, you do need to obtain a mechanical license.