
Hey Bas,
You would use the Instagram REST API to get the data and display your images as you want. While all REST API's are slightly different (Facebook, Twitter, Instagram or even WP REST API), they all share a common ground and once you have worked with one, you can work with pretty much any. REST API data can usually be fetch using various languages, you will be looking at the PHP library (or perhaps JS library depending on how you implement it).
Depending on how far you want to take it, working with API's can get complex. If you are using the PHP library, you should make sure that you cache API responses (using WordPress Transients for example) to avoid making API calls on ever page load which would delay the page load and throw an error if not accessible. You may also do it via AJAX to avoid long load delay when API calls are made, or even pure JavaScript if you are rendering your content using JSX for example.
My advise would be to search for tutorials "Instagram API integration tutorial WordPress", you will see that the 10 first results are quite spot on (this one for example).
Good luck with it 😉

Morning Thierry, Thanks for your quick response. As I am not familiar with using API I will have to dive into it :-).
Bas