You can renew your long-term residence permit 4 months at the earliest (before it expires). For extension of your stay you will need to arrange following documents to prolong your residence permit:

• Hosting Agreement - original or a certified copy, not older than 180 days, ask HR to issue
• Committment of the Organization - original or a certified copy, not older than 180 days, ask HR to issue
• Proof of accommodation – original or a certified copy, not older than 180 days, in Czech or billingual
• Copy of your passport
• Copy of your current residence permit card
• Green application – to be filled out in Czech, sent to Welcome Office to check it, check your country code here
• 2500 CZK stamp – available at the post office
  • it is called "kolek", it looks similar as the postage stamp and you'll probably get 3 because there is no stamp of 2500 value. They usually give people 2 stamps for 1000 Kč and 1 stamp for 500 Kč
• Copy of your health insurance card

When you have all the documents ready, send them by a registered letter ("doporučený dopis") to the following address:

Ministerstvo vnitra
Oddělení pobytu cizinců Jihomoravský kraj
Tuřanka 1554/115b
627 00 Brno