Change MySQL PDO connection to a WPDB connection

You need to repalce the PDO connection object with WPDB object. And for the kind of query in your example, looks like the best way to do it is with $wpdb->getcol. Something like this (didn’t test):

if ( isset( $_GET['term'] ) ){
    global $wpdb;
    $term = filter_var( $_GET['term'], FILTER_SANITIZE_STRING, FILTER_NULL_ON_FAILURE );
    if ( is_null( $term ) ) {
        echo json_encode( array() );
    } 
    else {
        $return_array = $wpdb->get_col( 
             $wpdb->prepare( 
                 "SELECT supplier_company 
                 FROM {$wpdb->prefix}_teleapo_supplier 
                 WHERE term = %s",
                 $term
             ) 
        );
        $return_arr = $return_arr ? $return_arr : array();
        /* Toss back results as json encoded array. */
        echo json_encode( $return_arr );
    }
}