The new button is not available when attempting to publish a new application at the OU or GPO levels

When attempting to publish a new application at the OU or GPO, the New button is not available. The administrator is unable to publish new applications, although they can see existing ones.

Set the "Allow application definition to be modified by users" to yes for any administrator user.  The user preference will override the preference set at the OU and the administrator will be able to add applications.