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In this work, we continue the study of the central region of NGC 613 by da Silva et al. (2020), by analysing the stellar and gas kinematics and the stellar archaeology in optical and near-infrared data cubes. The high spatial resolution of the Gemini Multi-Object Spectrograph (GMOS) data cube allowed the detection, using spectral synthesis methods, of an inner circumnuclear ring, with a radius of $\sim$ 1 arcsec, composed of $\sim$ 10$^9$-yr stellar populations. Such a ring is located between the nucleus and the circumnuclear ring composed by H II regions detected in previous works. Besides that, there is a stellar rotation around the nucleus and the rings follow the same direction of rotation with different velocities. The intensity-weighted average stellar velocity dispersion at the centre is 92 $\pm$ 3 km s$^{-1}$. Three distinct gas outflow components were detected. The direction of the outflow observed with the H $α$ emission line is compatible with the direction of the previously observed radio jet. The direction of one of the outflows detected in the [O III]$λ$5007 emission coincides with the axis of the ionization cone. There is no difference regarding the stellar populations and the stellar kinematics along the double stellar emission, probably separated by a dust lane as mentioned in Paper I, confirming that they are part of the same structure.