SharePoint audience group does not show up in Audience Targeting but you can easily search for that in people picker and provide access in SharePoint site.
Now it makes sense that, people picker was able to pick a newly created AD group but Audience picker cannot find that group unless an Incremental/Full sync is performed.
Some other groups might also be missing in Audience picker. It all comes down to what OU’s you pick up while configuring User profile synchronization service in SharePoint.
Resolution: If you cannot find your newly created Active Directory group in Audience picker while trying to set up audience targeting for a web part,
1. Make sure atleast one user is added to that AD group
2. Perform an incremental/Full profile synchronization
AD group will show up in Audience picker after a user profile synchronization.