Some states have no restrictions at all. Others impose earnings limits that, if exceeded, can reduce or suspend their retirement benefits. These limits can be annual earnings caps or based on a percentage of their retirement benefit. Some states may also have different rules for part-time versus full-time employment.
To determine the specific limits for a retired teacher, you need to check the regulations of the specific state's retirement system where they retired. The retirement system's website is the best place to find this information, or contacting the system directly.