Add a form field to one of the sections in Table Rate method

betrs-add-settings-field.php

/**
 * Add form field to 'Additional Options' section in the Table of Rates
 *
 * @return string
 */
function betrs_add_settings_field( $settings ) {
    // array of shipping provider codes
    $shipping_carriers = array( 
        'usps'  => 'US Postal Service',
        'fedex' => 'FedEx',
        'ups'   => 'UPS'
    );

    $settings['other']['settings']['shipping_carriers'] = array(
        'title'             => __( 'Carrier Selection', 'be-table-ship' ),
        'type'              => 'multiselect',
        'class'             => 'wc-enhanced-select',
        'default'           => '',
        'options'           => $shipping_carriers,
    );

    return $settings;
}
add_filter( 'woocommerce_shipping_instance_form_fields_betrs_shipping', 'betrs_add_settings_field', 10, 1 );