BuddyPress.org

I looked at the code for the plugin ‘Events Manager’, and managed to put together the following which worked for me:

    function setup_group_nav(){
    	global $bp;	
    	/* Add some group subnav items */
    	$user_access = false;
    	$group_link = '';
    	if( bp_is_active('groups') && !empty($bp->groups->current_group) ){
    		$group_link = $bp->root_domain . '/' . bp_get_groups_root_slug() . '/' . $bp->groups->current_group->slug . '/';
    		$user_access = $bp->groups->current_group->user_has_access;
    		bp_core_new_subnav_item( array( 
    			'name' => __( 'Custom', 'custom'),
    			'slug' => 'custom', 
    			'parent_url' => $group_link, 
    			'parent_slug' => $bp->groups->current_group->slug,
    			'screen_function' => 'bp_group_custom', 
    			'position' => 50, 
    			'user_has_access' => $user_access, 
    			'item_css_id' => 'custom' 
    		));
    	}
    }
    add_action( 'bp_init', 'setup_group_nav' );
    
    function bp_group_custom() {
    	add_action('bp_template_title', 'my_new_group_show_screen_title');
    	add_action('bp_template_content', 'my_new_group_show_screen_content');
    	
    	$templates = array('groups/single/plugins.php', 'plugin-template.php');
    	if (strstr(locate_template($templates), 'groups/single/plugins.php')) {
    		bp_core_load_template(apply_filters('bp_core_template_plugin', 'groups/single/plugins'));
    	} else {
    		bp_core_load_template(apply_filters('bp_core_template_plugin', 'plugin-template'));
    	}
    	
    }
    	
    function my_new_group_show_screen_title() {
    	echo 'New Tab Title';
    }
    	
    function my_new_group_show_screen_content() {
    	echo 'New tab page content';
    	
    }