ContactAfterInsert Class

public class ContactAfterInsert {
    public static void setContactDeptIT(List<Contact> cons){
        List<Contact> consToUpdate = new List<Contact>();
        
        for(Contact conInTrigger : cons){
            Contact c = new Contact(Id = conInTrigger.Id, Department = 'IT');
            consToUpdate.add(c);
        }
        
        update consToUpdate;
    }
}

ContactAfterTrigger

Trigger ContactAfterTrigger on Contact (after insert) {
    ContactAfterInsert.setContactDeptIT(trigger.new);
    /*Logic Moved to ContactAfterInsert class
    List<Contact> consToUpdate = new List<Contact>();
    
    for(Contact conInTrigger : trigger.new){
        Contact c = new Contact(Id = conInTrigger.Id, Department = 'IT');
        consToUpdate.add(c);
    }
    update consToUpdate;
	*/
}