If your Device's USB-C Port does offer Display Output mode, and there no signal on HDMI out of hyperdrive, please help to check:
-The length of the HDMI cable can not exceed 2 meters.
-Some manufacturers make its cable so that one end has to be connected to a display monitor, and the other end is connected to the source. Normally, the end to display monitor has a "TV" marked on it.
-HDMI has to connect to an HDMI display monitor with HDMI to HDMI cable. It is not compatible with the DVI/ Display port or other non-HDMI monitors, even with an adapter. You will need an Active Converter that can correctly convert the signal.
-Make sure your Display is set to correct HDMI input source.
-Test the HDMI Cable and Monitor/TV/Display to ensure they are also functioning properly.
-Turn off / Reset your USB-C Device, unplug then reconnect the Hyperdrive. Also switch off then unplug the Monitor/TV/Display and try to reset the connections to try again.