MySQL 8.0

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CREATE TABLE wp_posts (post_content text);
INSERT INTO wp_posts VALUES
  ('https://www.affiliate.com/redirect.php?tt=el&amp;store_id=this_is_the_store_id&amp;param1=this_is_param_1&amp;url=https://redirect_the_visitor_to_this_url.com&amp;c_id=id_of_the_campaign'),
  ('https://www.affiliate.com/redirect.php?tt=el&amp;store_id=this_is_the_store_id&amp;c_id=id_of_the_campaign&amp;param1=this_is_param_1&amp;url=https://redirect_the_visitor_to_this_url.com'),
  ('https://www.affiliate.com/redirect.php?tt=el&amp;store_id=this_is_another_store_id&amp;c_id=id_of_the_campaign&amp;param1=this_is_param_1&amp;url=https://redirect_the_visitor_to_this_url.com')
;

Records: 3  Duplicates: 0  Warnings: 0


UPDATE wp_posts
SET post_content = REGEXP_REPLACE(
  post_content,
  'https://www\\.affiliate\\.com/redirect\\.php\\?(?=.*\\bstore_id=this_is_the_store_id\\b)(?=.*\\bc_id=([^&]*))(?=.*\\burl=([^&]*)).*',
  'https://newaffiliate.net/c/1234/5678/9012?campaign=$1&u=$2'
)

Rows matched: 3  Changed: 2  Warnings: 0


SELECT *
FROM wp_posts


post_content


https://newaffiliate.net/c/1234/5678/9012?campaign=id_of_the_campaign&u=https://redirect_the_visitor_to_this_url.com

https://newaffiliate.net/c/1234/5678/9012?campaign=id_of_the_campaign&u=https://redirect_the_visitor_to_this_url.com

https://www.affiliate.com/redirect.php?tt=el&amp;store_id=this_is_another_store_id&amp;c_id=id_of_the_campaign&amp;param1=this_is_param_1&amp;url=https://redirect_the_visitor_to_this_url.com