Notify Jenkins of new post on WordPress

Take a look at some of WordPress’s Actions & Filters – in particular, you might want something like publish_post:

function my_custom_post_action( $post_id, $post ) {
    // Send out data to your service using something
    // like wp_remote_request:
    // https://codex.wordpress.org/Function_Reference/wp_remote_post
}

add_action( 'publish_post', 'my_custom_post_action', 10, 2 );

You may need to ensure that the post is actually “new”, as this hook will be triggered any time a post’s status is changed to “publish”. The Action/Filter reference has a lot of other hooks you can use that are related to posts.