The question of support for Microsoft Edge Browser has been asked of HPE/Micro Focus in the past. I am adding a link to an article from the Micro Focus Knowledge base where this question was asked for version 12.21. There are no plans to support Edge in any version of QC/ALM 12.x. There could possibly be support for it in version 14 however; R&D for HPE/Micro Focus will not answer that question. The QC/ALM client currently uses Active X technology and MS Edge does not support Active X.
Here is a link to the System Requirements page for QC/ALM that contains a list of the currently supported browsers for each version of ALM going back to version 11.