The new accelerator complex Nuclotron-based Ion Collider fAcility (NICA) is under development and construction at JINR, Dubna now (Fig. 1). This complex is assumed to operate using two injectors: the Alvarez-type linac LU-20 as injector of light ions, polarized protons and deuterons and a new linac HILAc - injector of heavy ions beams. Old HV fore-injector of the LU-20, which operated from 1974, was replaced by the new RFQ accelerator, which was commissioned in spring 2016. The first Nuclotron technological run with new fore-injector was performed in June 2016 with beams of D ⁺ and H2 ⁺ . The polarized deuterons beam were successfully injected and accelerated in the Nuclotron ring during the last run #53. Main results of the RFQ commissioning and the last Nuclotron run with new fore-injector are presented in this paper.