We present a study of the radio and optical properties of the high-frequency peaker (HFP) blazar PKS 1614+051 at z=3.21 based on the data covering the time period of 1997-2024. The radio data are represented by the almost instantaneous 1-22GHz measurements from the SAO RAS RATAN-600 radio telescope, the 5 and 8GHz data from the IAA RAS RT-32 telescopes, and the 37GHz data from the RT-22 telescope of CrAO RAS. The optical measurements in the R band were collected with the SAO RAS 1-m Zeiss-1000 and 0.5-m AS-500/2 telescopes, and the ZTF archive data. We have found low overall variability indices (0.1-0.2) and a median spectral peak at 4.6GHz, which is stable during the long-term period of monitoring. An analysis of the radio light curves reveals significant time delays (0.6 to 6.4 yrs) between the radio frequencies along with variability timescales ranging from 0.2 to 1.8 yrs in the source's rest frame, which is similar to the blazars at lower redshifts. Spectral modeling suggests the presence of both synchrotron self-absorption (SSA) and free-free absorption (FFA) processes. Based on the SSA model, we provide estimates of the magnetic field strength which peaks at approximately 100mG. A spectroscopic study with the BTA SCORPIO-1 spectrograph has found evidence of the regular motion of a neutral hydrogen envelope around the blazar center, which confirms the presence of enough gaseous matter to form an external FFA screen. The results highlight the importance of multi-wavelength and long-term monitoring to understand the physical mechanisms driving the variability in high-redshift blazars.