Yes, hair that has been transplanted through a hair transplant procedure can go grey over time, just like natural hair. The color of your hair is determined by the pigment-producing cells called melanocytes in the hair follicles. As you age, these melanocytes may become less active, resulting in a gradual loss of pigmentation and the development of grey or white hair.
Hair transplant surgery involves moving hair follicles from one part of your body (usually the back of the head, where hair is typically more resistant to the effects of hair loss) to another area with thinning or balding hair. The transplanted hair will retain its original characteristics, including its potential to go grey as you age.
As a result, just like the rest of your natural hair, the transplanted hair may eventually turn grey. The rate at which this happens can vary from person to person and is primarily determined by genetics and the aging process.