My NTS expire in 8 Aug for REG, but I think i will take the exam at the end of August or beg of September, so can I apply for a new NTS after the expiration of the old one and take the exam in the same window?
Yes, you can let your NTS expire, apply for a new one, receive a new one, and schedule your test. It doesn't matter that your old NTS expired within the same testing window. The limit is only in taking the exam once per window. It depends on your state how quickly you get the new NTS, so apply as soon as you can after the expiration.