BE-400 pilot reported horizontal stabilizer de-ice system failure in flight. Returned to departure airport and landed uneventfully.

Narrative

Suffered delayed departure due to weather; once the active precipitation at the surface stopped we dispatched. We conducted a full ops check of aircraft anti icing equipment in taxi and all systems checked good. Conducted a normal takeoff with initial clearance to climb to 4000 ft. In climb between 500 and 1000 ft. we activated all aircraft anti ice equipment and received an immediate 'H stab ice fail' annunciation. We leveled at 4000 ft. momentarily where we were below the ceiling but in significant mixed icing conditions; probably moderate icing. We [requested priority] with ATC and requested a lower altitude; were cleared down to 2000 ft. We then requested and received vectors to the ILS XXL at ZZZ. We conducted the H stab de-ice system failure" checklist and conducted a flap 10 landing with no further issues. Post flight inspection we found trace ice on the leading edge of the tail. We conducted the ground checks of tail de-ice system in taxi and it passed. We used the tail de-ice system inbound the night prior with no issues. The aircraft was kept in a hangar overnight. I am not aware of any further actions we could reasonably take that would prevent this mechanical failure or help us become aware of it prior to takeoff. MVFR at the surface; approximately 4000 ft. ceiling with light to moderate icing conditions up to around 8000 ft. or higher."