You can install Compliance for Confluence Cloud in two ways; through the Atlassian Marketplace or within Confluence using the Universal Plugin Manager (UPM).
For both methods, you will need your Administrator’s permission to install the app to your Confluence.
Atlassian Marketplace
Go to the Atlassian Marketplace listing and click Try it free. Then, select Cloud version and site where to be installed.

Within Confluence, click Apps in the top navigation and click Find New Apps in the drop down menu. Search for “Compliance for Confluence” and the app should appear in the search results.

Once installed, you will be able to open Compliance from the Apps dropdown menu.