This psychotherapist guy is different from all the other main characters. He doesn't change. If this were a science class—and hey, this is a science fiction novel—Stern would be the "control" variable whose reliable, steady behavior contrasts with all the other folks, from the sci-fi gestalt to the tormented Kews. He represents homo sapiens, the ordinary human species, the one that isn't More Than Human and seems a lot less crazy.
Stern guides Gerry in remembering his past, his murder of Miss Kew, and his nature as a gestalt organism. Stern is something of a textbook psychoanalyst, revealing almost nothing about himself and just listening to Gerry or providing the occasional prompt or theory for the teen to do the bulk of the therapeutic work himself. Yep, Stern believes the patient should do the work in psychotherapy. He tells Gerry:
The only thumbnail [description of psychiatry] you'll get from me is this: no one knows what's really wrong with you but you; no one can find a cure for it but you; no one but you can identify it as a cure; and once you find it, no one but you can do anything about it. (2.2.3)
Stern's job is just to listen and prompt. Freud would be proud.
Near the end of Gerry's session, Stern tries to convince Gerry that the teen's gestalt needs morality. The psychotherapist has a noble aim. He tells his patient that the gestalt is alone but can live better by choosing morality. Stern fights hard to open Gerry up to this possibility, but fails.
Stern does have one trick up his sleeve: that tape recorder. Now before you start griping about how tape recorders are so old school, remember this book was written in 1953. Stern secretly records Gerry saying that memory-block "Baby is three" phrase, and then plays it back to the teen to push him deeper into his memories. That's not a superpower, but it is a use of science to solve a problem. Pretty fitting for a science fiction book.
At the end of their session, Gerry wipes Stern's memory and resets his office back to the way it was before he entered. This further emphasizes just how normal Stern is: nothing from his time with Gerry changed him. Stern's role as Gerry's therapist in Part 2, the only other person there in the office, makes his unchanging presence a big factor in the novel.