To make it so that when you click on an email link a new compose message window opens up in Gmail, you need to complete a couple of steps, depending on the browser you are using.
If you use Chrome as your default browser all you need to do it log in to Gmail and look in the top right of the address bar for a double diamond symbol. Click that, select Allow and then click Done:
If you use Safari you will need to install this browser extension. Once downloaded, double-click on the file in your Downloads folder, click Install and then select Gmail from the options:
You then just need to quit Safari completely and reload it to get the extension to work.
Click on the “hamburger” button in the top right and then click Preferences:
Next, go to the Applications tab, search for mailto and then change the dropdown action to Use Gmail:
Then just close the Preferences window.