If you want to create a new arrangement of a public domain work, you are allowed to do so. In the United States, a work's copyright lasts for the author's life plus 70 years after death. Once this time has passed, the work becomes part of the public domain and is no longer protected by copyright. However, if a song's lyrics and music were published before 1926, then the song is in the public domain in the United States. For instance, the traditional Christmas carol "Deck The Halls" was published in the United States in the 1800s. If you create a new arrangement of this song, you can register it as the arranger but not as the composer or author.
It's essential to remember that a song may be in the public domain in the US but not in another country. Additionally, it would be best to ensure the version you're using is in the public domain. Other people may have created new arrangements of a public domain work, and that specific arrangement may not be in the public domain. Therefore, doing your research before using a public domain work is crucial.
It's also worth noting that public domain works may generate fewer royalties than original compositions. For example, BMI only pays 20% of the value of an original composition, whereas ASCAP pays 10%.