We present a study of the parsec-scale multifrequency properties of the quasar S4 1030+61 during a prolonged radio and {gamma}-ray activity. Observations were performed within Fermi {gamma}-ray telescope, Owens Valley Radio Observatory 40-m telescope and MOJAVE Very Long Baseline Array (VLBA) monitoring programmes, covering five years from 2009. The data are supplemented by four-epoch VLBA observations at 5, 8, 15, 24 and 43GHz, which were triggered by the bright {gamma}-ray flare, registered in the quasar in 2010. The S4 1030+61 jet exhibits an apparent superluminal velocity of (6.4+/-0.4)c and does not show ejections of new components in the observed period, while decomposition of the radio light curve reveals nine prominent flares. The measured variability parameters of the source show values typical for Fermi-detected quasars. Combined analysis of radio and {gamma}-ray emission implies a spatial separation between emitting regions at these bands of about 12pc and locates the {gamma}-ray emission within a parsec from the central engine. We detected changes in the value and direction of the linear polarization and the Faraday rotation measure. The value of the intrinsic brightness temperature of the core is above the equipartition state, while its value as a function of distance from the core is well approximated by the power law. Altogether these results show that the radio flaring activity of the quasar is accompanied by injection of relativistic particles and energy losses at the jet base, while S4 1030+61 has a stable, straight jet well described by standard conical jet theories.