Domain DNS cannot resolve External website

The domain is example.local and the dns server on serve1 has a forward lookup zone for example.org I created A host name in forward lookup zone folder example.org to point www.example.org to the external server (godaddy). The website cannot resolve on the domain unless i change the dns server to something public like cloudflare or google. How can i fix this without changing the name of the domain? Since the domain is example.local, why am i having this issue.