Higher order modulations are the key elements to the throughput and spectral efficiency increase, especially important for the limited bandwidth scenarios. In this paper, we present a detailed analysis of the 256-QAM signal demodulation performance for the novel sidelink (SL) mode of the 5G NR communication systems. The performance is frequency offset (CFO). It was shown that the CFO has critical impact on the system performance, along with channel mobility. The simple and effective CFO studied in the non-stationary, frequency selective channel in the presence of the carrier compensation algorithm based on the slot-by-slot time-domain signal processing is proposed and investigated. Obtained simulation results have shown the feasibility of the 256-QAM modulation in applications to the main 3GPP sidelink scenarios and parameters, with the proposed CFO compensation method applied even in the case of significant user mobility.