First of all, make sure you have the latest Chromium-based version of Edge installed. The new version has an icon like this:
Next, select Extensions from Edge’s toolbar menu (or enter
edge://extensions into the location bar). Select the option “Allow extensions from other stores” in the left-hand panel and click “Allow” when the confirmation dialog appears.
Now you can go to the Chrome Web Store and install the LeechBlock extension.
If you need more detailed instructions for installing Google Chrome extension in Microsoft Edge, go here.