The Elders are the leaders of the Order. They're veteran monster slayers and there are always 3 of them. Initially they appear as wise figures, guiding the recruits through their training and selecting Tim to be the first of them to be given a solo mission. However, after Tim's deception is exposed, they reveal themselves as having Nazi connections (Lesson One: Vampires).
It started with the previous trio of Elders, who allied themselves with the German National Socialist Party and started targeting monsters merely for being monsters regardless of whether they were harming anyone or not. After they were replaced, the current trio of Elders decided to maintain their goal of cleansing Humankind from these impurities. This made them even angrier when they found out about Tim. They escape before he can confront them properly for their betrayal of the Order's noble goals, but in Mummy Issues, they're back in charge at the Romanian secret headquarters.
At first, they were content with banishing him, though, worried that he might reveal their additional purpose to the other monster slayers, but when they made a mistake that got some humans maimed, they decided to blame it all on Tim and accuse him of sabotage. After this, they tasked Tim's former mentor, Ben, with getting him back... dead or alive (Mummy Issues)!