The international project “NICA” (Nuclotron-based Ion Collider fAcility) is an accelerator complex which is under construction at the Joint Institute for Nuclear Research (Dubna, Russia). Basing on the NICA project demands NRC “Kurchatov Institute” (Moscow, Russia) designed and manufactured two trial 12 kA 1G current leads (CLs) intended for powering of the JINR superconducting magnets test bench. The main requirements for the CLs were: a reliable and robust design, usage of liquid nitrogen from the NICA cooling circuits as a resistive section coolant, low resistance joints, current ramp rates up to 10 kA/s and the total heat load to the 5 K end not exceeding 0.4 W/kA per one CL. An in-situ cold test of the trial 12 kA CLs held at JINR in 2015 demonstrated the operational reliability of our technological approaches. Following the successful test results the serial production of 20 pairs of 10.5 kA HTS CLs with very few design updates for the accelerator powering started. The first 10 pairs were fabricated, tested and shipped to JINR as a part of the NICA commissioning framework in June 2017. All the CLs fulfilled the acceptance test requirements. The production of the remaining 10 pairs is to be finished in 2018. The paper gives an overview of the 12 kA and 10.5 kA HTS CLs’ design, discusses their thermal, magnetic and electrical characteristics and presents the acceptance tests results. We also compare our CLs with earlier works by other groups in the context of HTS stack-and-soldering technique, joints’ resistances, relative heat loads into the cryogenic environment etc.