In functions.php child theme include template-tags.php from parent theme:
require_once get_theme_file_path( '../parent-theme/inc/template-tags.php' );
In the child theme template-tags.php remove parent action and add the child action replacing it:
remove_action( 'tag', 'parent-function', 0 );
add_action( 'tag', 'new-child-function', 10 );