The installation of the application needs to be done by the main admin of your HelpDesk license (the license creator email address) and latter authorised with Jira administer account.
Please go to Marketplace, find Jira for HelpDesk and proceed with adding it to the cart. Once the checkout is done, click "Install" in the top right corner to finalize the installation.
After the integration is installed, it should be displayed as the ticket details section widget of your HelpDesk agent application. Open it and authorise with your Jira and HelpDesk accounts. If one of the buttons is gray, it means that one of the accounts is already authorised.