From the Tribune‘s chimps-in-the-media story:

“As entertainers, they are washed up by age 5, 6, or 7, and what happens to them then?” New said. “They have another 50 or 60 years of life ahead of them. … They could get sold to roadside zoos, as private pets or whatever.”

Why, I’m glad you asked! Some of them go to retirement homes. More here, here, and here. Space monkeys apparently have their own retirement home.