Once the initial 30 days trial period is over, the JIRA Universal Plugin Manager doesn't provide any button to request an extension of the trial period. However, you can request a new trial license key manually.
- Open the Atlassian Marketplace
- Click the 'Free 30 day trial' button, it takes you to your my.atlassian.com account
- Enter the name of your company and click the 'Generate license' button
- Copy the generated license
- Go to the JIRA Universal Plugin Manager to display the add-on information
Edit the license key and paste your new license over the previous one