It is with great courage that a worship leader deviates from the traditional Christmas carols at Christmas but there may be situations which call for a new song.
Churches that use more contemporary music in particular might be seeking something to add to the expected repertoire. If that is your church then consider the offerings from the website worshiptogether.com. If you put “Christmas” in the search box you will get no less than 240 results. Some that rise to the top in my mind is Emmanuel/Hallowed Manger Ground (Ed Cash/Christ Tomlin, 2009), Born in Bethlehem (Third Day, 2006), Joy Has Dawned (Getty/Townend 2004). How Many Kings (Marc Mantel/Jason Germain, 2006) is another great song; though not on this website it is available in the latest Advent issue of Reformed Worship. Some of these songs do not use inclusive language for people; sometimes you can receive permission to change the text but not always.
If you are looking to add a global song to your repertoire consider In the Heavens Shone a Star from the Philippines (Global Songs for Worship #28).
As for new hymns, a great first place to look is at the hymnals on your shelf. On the web consider the offerings of the online hymnody through Hope Publishing. If you put “Christmas” in the theme search box you will receive a list of 193 hymns with the newest offerings highlighted in Green and best sellers in Purple. All the music on this site is downloadable if you have a valid CCLI or Onelicense.net copyright license. You may also contact Hope for permission for a one time use.
What is your church singing this Advent/Christmas season? Are you considering teaching any new songs? If so, which ones?