You can use the JIRA DVCS plugin to scan commits and pull requests, creating relevant metadata and hyperlinks in any mentioned JIRA Issues.
GitHub Enterprise settings
In the top right corner of any page, click your profile photo, then click Settings.
If you'd like to link the JIRA DVCS plugin with an organization, click the name of your organization in the left sidebar.
In the user settings sidebar, click Applications.
At the top of the page, under Developer applications (for a user account) or Organization applications (for an organization account), click Register new application.
Under Application name, type "JIRA".
Under Homepage URL, type the full URL to your JIRA instance.
Under Authorization callback URL, type the full URL to your JIRA instance.
Click Register application.
Under Developer applications, note the "Client ID" and "Client Secret" values.
On your JIRA instance, log into an account with administrative access.
At the top of the page, click the Settings ("gear") icon.
From the dropdown menu, choose Add-ons.
In the left sidebar, under Source Control, click DVCS Accounts.
Click Link Bitbucket or GitHub account.
Under Host, choose GitHub Enterprise from the dropdown menu.
Under Team or User Account, type the name of your GitHub Enterprise account.
Under OAuth Key, type the "Client ID" shown for the developer application you created earlier on GitHub Enterprise.
Under OAuth Secret, type the "Client Secret" shown for the developer application you created earlier on GitHub Enterprise.
If you don't want to automatically link new repositories owned by your GitHub Enterprise account, unselect Auto Link New Repositories.
If you don't want to enable smart commits, unselect Enable Smart Commits.
Review the permissions that you are granting to your GitHub Enterprise and click Authorize application.
If necessary, type your password to continue.
Your repositories should now be listed on the DVCS Connector page.