This could depend on where they work as well as their personal choices, but in general, I would say no. If they work alongside police and are employed by police departments, potentially. However, if they work in a psych hospital, jail/prison facility, or in private practice then likely no, they do not.
However, if they have a conceal carry for their own protection (at their private practice or walking to and from their car) that is entirely different because it is a personal choice rather than a career-based requirement.
Forensic psychologists carry guns due to the nature of their intense field work and for the safety. Sometimes they are even required to carry firearms from work.
No because they are not law enforcement officers.