Can I change my Relative Permit to a Quota Permit so that I can apply for a Permanent Residence Permit?

The long answer

The Quota Permit no longer exists: after a 2014 change to the Immigration Act, the Quota and Exceptional Skills permits were replaced by the Critical Skills Permit which was valid for up to five years. 

An updated Critical Skills list was published in 2017 and again in 2020. Although the list is often amended after publication, teachers were not mentioned in either the 2017 or the 2020 list. This would mean that you would not be eligible to apply for a Critical Skills permit, which is unfortunate as this permit automatically makes you eligible to apply for permanent residence.

Perhaps you should look again into applying for a Spousal Permit which is also a permanent residence permit, if your husband is a South African citizen or a permanent resident. You need to have been married for at least five years, and your husband would need to write a letter supporting the application. His identity document would also be required with the application, and if he is a permanent resident, a copy of his permanent residence permit. 

It takes a long time for Home Affairs to issue a spousal permit - it can take over two years - and in the present time, it could take even longer.  

It might be worth asking one of the following organisations for help in getting your application processed, as they have had a lot of experience in dealing with the endless delays that so many people experience at Home Affairs:

Legal Resources Centre
Email: info@lrc.org.za
Tel: Cape Town: 021 481 3000
Tel: Johannesburg: 011 836 9831  

Lawyers for Human Rights
Tel: Cape Town: 021 424 8561
Johannesburg Office and law clinic
Tel: 011 339 1960