New mac but want to use time machine and erase old mac files

I have a new mac and want to use time machine. I have an external drive that I used for the old mac. I want to use that external drive for my new mac. I chose not to inherit old backups when I first used time machine for new machine and now I think it's keeping the backups for the old machine because there's not enough space for a backup now. I don't want to keep the old backups from the old machine. Do I have to reformat the external drive or something? If the answer is yes, please give instructions. If it's something else, please also give instructions. Much appreciated.