Hi Christian. Thanks for your detailed question.
Please try this custom CSS:
body.single-tribe_events .tribe-events-sub-nav {
display: none;
}
You can add custom CSS code via your child theme’s style.css file or via a plugin like Simple Custom CSS or, my favorite, Jetpack. Jetpack supports regular CSS and the LESS and Sass pre-processors.
If you’re not a CSS expert, Jetpack’s Custom Design reference may prove helpful.
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If it doesn’t work for you, please provide a link to one of your events you’d like the prev/next navigation removed from.
Thanks!