Application of army nursing last date has already passed for this year. You can apply again next year. Form will expectedly release on 2nd week of Nov.
The notification for Indian army B.Sc Nursing for 2021 will release 2020, although the dates are not known. The exam is conducted once in a year by DTE general medical services (army) for admission in B.Sc Nursing. So you need to wait until official notification is released.