get_terms() accept an array of arguments as second parameter. One of those parameters are include
include(integer) An array of term ids to include. Empty returns all.
You already have your selected term ids in an array, so just simply pass them to the include parameter in the array of arguments in get_terms()
$terms = get_terms( $taxonomy, array( 'include' => $term_id_array ) );
or with short araay syntax (availble since PHP 5.4)
$terms = get_terms( $taxonomy, ['include' => $term_id_array] );