ActiveAdmin's master now includes a Pundit authorization adapter. If you are using the master branch of ActiveAdmin, Pundit can be easily utilized. Otherwise you can manually add the existing pundit_adapter.rb to older versions of ActiveAdmin, although more work might be required.
See ActiveAdmin PR #2857 for more context and detail on how the adapter was added.
After ActiveAdmin is setup to use the Pundit authorization adapter, it does check the authorization for the default resource actions: show, index, edit, update, new, create, destroy. Any custom actions must be manually authorized.
One detail to check is that your Pundit policy defines the methods expected by ActiveAdmin. There is a template available to be used as a starting point. The ActiveAdmin authorization docs may also be helpful.