I do think a therapist with some background in gifted children would be helpful, though given your son's previous experience, it sounds like finding someone who is a good fit is more important. I always tell people (especially children) that they need to go to the intake with the expectation that they are interviewing the therapist, and may need/choose to go to several therapists before they find someone they are comfortable with. As a parent, you guys can sit down with your son and go over some of the surface screening tools to give him and yourselves some insight. Here's the ones I would suggest:
Vanderbilts (ADHD): https://www.nichq.org/sites/default/files/resource-file/NICHQ_Vanderbilt_Assessment_Scales.pdf
SCARED (anxiety): file:///C:/Users/tessaw/Downloads/Screen%20for%20Child%20Anxiety%20Related%20Disorders%20Child%20Version.pdf
PHQ-9 (Depression): http://www.cqaimh.org/pdf/tool_phq9.pdf
I would also suggest conversations with him (which you have probably already had) about how stimulated he is at school. If he has a desire to be challenged, and is bored instead, it might mean an environmental issue rather than internal.
Good luck!