The status of the development of the Level-0 endcap muon trigger system for the ATLAS experiment at the HL-LHC is presented. The upgraded system reconstructs muon candidates with an improved p T resolution by combining data from various subdetectors. This is realized by exploiting the evolution of the data transmission technologies, to send all hit data of Thin Gap Chambers (TGCs) and the data of other subdetectors to the counting room. Primitive muon candidates are reconstructed using track segments reconstructed from hit data of TGCs. An initial implementation of the TGC track segment reconstruction with firmware for an FPGA is tested, and it is verified that muon candidates are successfully reconstructed for ideal cases. The trigger efficiency is estimated with a software algorithm and using a Monte Carlo simulation. The efficiency is estimated to be higher than 90% for the threshold of p T > 20 GeV and the endcap region. The trigger rate is estimated with a software algorithm and using pp collision data, which are overlaid to emulate the high pileup condition at the HL-LHC. The rate is estimated to be lower than 25 kHz for the threshold of p T > 20 GeV and the endcap region. This evaluation does not include the precise determination of p T using Monitored Drift Tube (MDT) hits, and the trigger rate is expected to decrease with its inclusion.