The LHC is expected to increase its center-of-mass energy to 14 TeV and an instantaneous luminosity to $2.4\times10^{34} \rm cm^{-2} \rm s^{-1}$ for Run 3 scheduled from 2021 to 2023. In order to cope with the high event rate, an upgrade of the ATLAS trigger system is required. The level-1 endcap muon trigger system identifies muons with high transverse momentum measured by a fast muon trigger detector, TGC. In the ongoing upgrades for Run 3, new detectors called the New-Small-Wheel (NSW) and RPC BIS78 will be installed in the inner station region for the endcap muon trigger. Track information from the NSW and RPC BIS78 can improve the performance of the level-1 endcap muon trigger system significantly due to their good resolutions. In order to handle data from the TGC and new detectors, some new electronics have been developed, including the trigger processor board known as Sector Logic (SL). The SL board has a modern FPGA with huge resource, making it possible to implement algorithm for trigger decisions. A charge identification algorithm has been developed newly and the accuracy is estimated by simulation. Also, a trigger algorithm with NSW has been developed to reject fake triggers and improves the transverse momentum resolution. The trigger rate was estimated by real data in Run 2.