Is Pap smear required after radical hysterectomy surgery?

No, there is no need now- there is no cervix to take the smear from- in case a total hysterectomy was done. If there are any symptoms of discharge or bleeding still from the remaining vagina- in that case, she may need to be examined and tests like a vaginal swab/ colposcopy required. (A rare situation, a post hysterectomy complication, or a fresh vaginal complaint later on, if still sexually active).