First you need to determine whether the mounting brackets are Honda (less likely) or aftermarket (more likely), such as Thule or Yakima. Is there a company logo on the brackets?
Aftermarket racks have vehicle-specific "landing pads" and towers that accept standard crossbars. It sounds like the last owner kept the crossbars, knowing they could be reused. In that case you need only get the correct crossbars (Thule crossbars are square; Yakimas are round), which are available separately. Many Element owners choose 58" crossbars, but you can also go longer or shorter.