If you receive a NOC this means your visa has already been cancelled. You may be given the opportunity to apply for this decision to be revoked (or reversed). In some cases you will have the opportunity to seek an appeal at the AAT. It is important to take advantage of this opportunity if you have strong grounds for remaining in Australia or if a mistake was made when your visa was cancelled.
After you have had a visa cancelled in Australia there are limited options of other visas you can apply for without first leaving the country. If your visa was cancelled due to Character Issues it will be very difficult to be granted another visa. You may have an option to seek Ministerial Intervention where all other avenues have been pursued.