Since the Music Modernization Law, it is no longer necessary to obtain a license to distribute a cover to streaming platforms.
You can distribute a cover as long as your version is faithful to the original in terms of lyrics, melody, and structure. If you stray too far from the original version, your song will no longer be considered a cover and further legal action will be necessary. Yes, you can take liberties with style and fit.
Please note that remixes or mash-ups are not considered covers and require a separate license.