A variety of people can serve as the school's (LEA) representative. It is not imperative for there to be a director of special education. Often the principal will serves as the school's representative. It is important that whoever is representing the school be authorized to allocate resources. Sometimes a school counselor or a special education case manager will "act" as the representative however often these individuals are often not able to authorize spending and as a result, the can not act as the school's representative.
Here is a good article that describes the role of the LEA representative: https://awsa.memberclicks.net/update-article--role-of-lea-representative-in-iep-meetings--supporting-ccr-ieps
The Individuals with Disability Education Act (IDEA) 2004 identifies the LEA representative as someone who;
(i) is qualified to provide, or supervise the provision of, specially designed instruction to meet the unique needs of children with disabilities;
(ii) is knowledgeable about the general education curriculum; and
(iii) is knowledgeable about the availability of resources of the public agency.
(34 CFR 300.321(a)(4))