MariaDB 10.3

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create table wpbz_posts
(post_content VARCHAR(100));
insert into wpbz_posts values ('<xml>abc<h1>bla</h1>def<h1>bla</h1></xml>')
select * from wpbz_posts

post_content

<xml>abc<h1>bla</h1>def<h1>bla</h1></xml>

UPDATE wpbz_posts 
SET post_content = REGEXP_REPLACE(post_content,'<h1>.*?</h1>','') 
WHERE post_content LIKE '%</h1>%'

Rows matched: 1  Changed: 1  Warnings: 0

select * from wpbz_posts

post_content

<xml>abcdef</xml>