Don't remove any backups. That may disrupt the Time Machine indexing and data base and make it impossible to restore from the backup disk.
Let TM machine handle the management of the disk space. It may inform you that the disk is full and indicate that it is deleting older backups, or ask you permission to delete older backups. That will enable you to continue using it for backups. If it indicates that it is unable to make sufficient space for a new backup, at that point keep the full Time Machine drive as an archive for older backups, and obtain a new drive and start a new backup set with the new drive. You might consider getting a larger drive for future backups when that happens.