Norris grew up near Fultondale, graduating from Phillips High School in 1951. He then signed up with the U. S. Navy, serving in the Korean War. Upon his discharge, he attended the University of Alabama and earned his law degree.
In 1975, Norris helped start Fultondale's first bank, Bank of Alabama. Now known as CapitalSouth Bank, the company later built a new bank adjacent to the original building. The original bank building was then converted into an operations and community center in 2005 and named the Palmer Norris Center. The recommendation for the center name came from Dan Puckett, chairman and CEO of Capital South. Norris was a member of the bank's board from 1975 until his death.
Norris' community involvement was not, however, restricted to banking. In his legal career, he served as special prosecutor for Morris, Warrior, and Homewood and as special assistant attorney general for the state. He was city prosecutor in Gardendale for more than 25 years and was city attorney and municipal judge for Fultondale from 1988 until his death.
Norris was also an active member of Gardendale's First Baptist Church, where he spent many years as a Sunday school instructor and was also a deacon. The class was unofficially known as the Norris Class until church officials attempted to name it officially the "older adult class." The class members did not wish to be named "older," so the Norris Class name became official. The class suspended lessons upon his death to reflect on his life and sing some of his favorite hymns.
Norris died in 2007 after a long illness. He was survived by his wife, two children, seven grandchildren, a brother, and a sister. He was buried in Walkers Chapel.
- Palmer "Pete" Norris obituary. (October 26, 2007). The Birmingham News.
- Singleton, William C., III. (November 4, 2007). "Norris left positive mark on northern area." The Birmingham News.
- "Palmer Norris Center" . (April 1, 2005). CapitalSouth Bank. Accessed November 5, 2007.