Note: Currently, you can only request a GitHub App from your organization owner when installing the GitHub App directly from the GitHub App owner, not when installing a GitHub App from GitHub Marketplace.
If you find a GitHub App on GitHub Marketplace that you want your organization owner to install, you must make the request from the GitHub App's public installation page. The URL for a GitHub App public installation page is https://github.com/apps/APP-NAME/installations/new, where APP-NAME is the name of the GitHub App.
Organization members can send a request for their organization owner to install a GitHub App on the organization. To do so, follow the steps outlined in "Installing a GitHub App from a third party." If you don't have permission to install the GitHub App on the organization, GitHub will send an email to the organization owner to notify them of the request. The organization owner can modify the repositories that you selected and choose whether to install the GitHub App.