Tasks for AWS can be installed and upgraded like any other regular add-on via the Universal Plugin Manager (UPM) (see Managing Add-ons for details):

Log into your Bamboo instance as an admin.
Click the admin dropdown and choose Atlassian Marketplace.
The Manage add-ons screen loads.
Click Find new add-ons from the left-hand side of the page.
Locate Tasks for AWS via search.
The appropriate add-on version appears in the search results.
Click Try free to begin a new trial or Buy now to purchase a license for Tasks for AWS.
You'll be prompted to log into MyAtlassian if you're logged out. Tasks for AWS begins to download.
Enter your information and click Generate license when redirected to MyAtlassian.
Click Apply license.
If you're using an older version of UPM, you can copy and paste the license into your Bamboo instance.

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