Display custom tags for custom post listing page

Taxonomies (and post types) need to be registered on init. You’re registering them on admin_init:

add_action( 'admin_init', 'gccsi_create_client_tax' );

This means the taxonomy isn’t registered on the front-end. Change the hook to init:

add_action( 'init', 'gccsi_create_client_tax' );