Both as a teacher and as a camp counselor, I have dealt with plenty of separation anxiety in older kids.
In early elementary kids, it is still common to have a transition period as a child enters a new classroom. Even if the child was perfectly happy in the classroom next door the year before, he may spend the first couple of weeks crying in his new classroom. Intellectually, he knows he was happy the year before and will probably be happy again, but in between then and now, he has spent a lovely, long summer in the bosom of his family. For him separation anxiety is wrapped up in feeling uncomfortable with a new routine. Once he has cycled through the weekly schedule a couple of times and feels he knows his teacher, he is fine.