add short description under price

Looking at the content-single-product.php of woocommerce github, I see that product excerpt is already supposed to be after price

/**
* Hook: woocommerce_single_product_summary.
*
* @hooked woocommerce_template_single_title - 5
* @hooked woocommerce_template_single_rating - 10
* @hooked woocommerce_template_single_price - 10
* @hooked woocommerce_template_single_excerpt - 20
* @hooked woocommerce_template_single_add_to_cart - 30
* @hooked woocommerce_template_single_meta - 40
* @hooked woocommerce_template_single_sharing - 50
* @hooked WC_Structured_Data::generate_product_data() - 60
*/
do_action( 'woocommerce_single_product_summary' );

So either your theme is removing this action or you are not using excerpts.

If you are not using excerpts adn you dont see theme for products, you can activate it under screen options tab (in the top right corner, if system language is LTR).

If you have excerpt and don’t see it you will need to hook into woocommerce_single_product_summary at priority between 11 and 29 (maybe even between 11 and 19 if some other action was hooked into priority 20).
For example

add_action('woocommerce_single_product_summary', 'bt_custom_product_description', 15);
function bt_custom_product_description () {
    echo 'Some description here';
}

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