Are there any Navy or Army clinical psychologist that became a psychologist while in the service?

Yes, you can do this in the Army. I was actually looking at this my myself. The Army will let you go to school if you are accepted into a program. I had a friend that did this and became a social worker with the Army. He still works in behavioral health. He was an officer already and then was accepted in a schools program for this. The Army paid for it while he was in school. He came back to the Army as a CPT. If you want to do this you will have to get your bachelor first. Then you would have to find a school and either go for your PsyD or PhD. When I was looking at it I was going to try PsyD. I wanted to stay on the clinical side. Keep in mind that is a long time. I spoke to an Army Psychologist about his experience. It is basically 7 years of schools before you are off on your own. I would try to go to your local post's Behavioral Health Office and see if you could speak with one as a means of professional development. That is what I did. I was able to call him and we spoke about it for a while.

There is a PsyD program the Army participates in that is EXTREMELY competitive. You're probably better off applying to the Master in Social Work program. If you are intent on being a Psychologist specifically, there are several hybrid programs out there you can attend. They require online course work with several conferences a year. Plus you still have to meet the experience requirements of 2000 hours which is equivalent to two years of part time intern work. The Army isn't going to pay you to go to any old Psychology program while you're on active duty and TA isn't allowed to be used for doctorate programs