As noted in my previous post, Microsoft Edge unfortunately does not support Tracking Protection Lists (TPL), a useful feature that was present in IE. Also the add-on support in Edge has been postponed several times, but there is still a solution to block ads in Microsoft Edge.
Hosts-based ad blocking. This is a long known method which was also used by some for blocking ads in IE. Hosts-based ad blocking has its advantages. It is transparent, standards based, does not require any add-ons and works in all browsers. On the downside, this approach only blocks 3rd-party content on the domain level and is not as flexible and powerful as TPL or in-browser solutions, but in practice, as my first tests show, works astonishingly well.
Give it a try and please report ad servers/sites which are not correctly blocked in order to improve the list over time.
Tip: You can now safely disable Flash in Microsoft Edge ;)