JIRA Connect works with HipChat and other applications. For example, you can use the “Share” function of JIRA Connect and send the complete URL to HipChat, E-Mail, Text Message, etc. This is a convenient way to send the URL directly out of the app. Alternatively you can use the copy function and paste the URL into any other application.
In addition JIRA Connect supports inter-app communication via URL Schemes. You can generate a link that starts with jira:// and JIRA Connect will be opened on your device. If you append a issue key such as jira://tst-123, the correct JIRA issue will be opened by JIRA Connect.
If you are on JIRA Server you can change your e-mail notification template so that users can open issues directly in JIRA Connect. Here are some instructions.