Welcome to Android Central! Are you talking about a playlist on Google Play Music, or was it a generic playlist file saved on the phone only? If it's a GPM playlist, then go to Google Play Music on your desktop browser and see if it's there in the Playlists category. It has to be the same Google account as the one you used on that old phone.
If it was only a generic playlist file saved only to that phone, and if you didn't back it up anywhere, then it's gone.