Using multi-wavelength imaging observation obtained from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO), we study the evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic topology. This fan-spine configuration is situated near the Active Region 12297 and is rooted in a nearby sunspot. The two layers of the cool plasma flows lift up from the fan plane in parallel and interact with each other at the maximum height of the elongated spine in the lower corona. The first layer of the plasma flow (F1) moving with a slow velocity (5 km/s) reflected from the spine’s field lines. Subsequently second layer of plasma flow (F2) with impulsive velocity (114-144 km/s) interacts with the first layer at the maximum height and generating the shear motion , which is responsible for the evolution of the Kelvin-Helmholtz instability inside the elongated spine. The amplitude and characteristics wavelength of the K-H unstable vortices increases, which satisfy the linear growing mode of this instability. Using linear stability theory of the K-H instability, we calculate the Alfvén velocity in the lower layer. We conjecture that the estimated shearing velocity is higher than the estimated the Alfvén velocity in the second denser layer, which also satisfies the classical criterion of K-H instability. The fan-spine configuration possesses magnetic field and sheared velocity component, we estimate the parametric constant [Λ≥1] which confirms that the velocity shear dominates and the linear phase of the K-H instability is evolved. The present observation indicate that in the presence of complex magnetic field structuring and plasma flows, the K-H instability evolve in the fan-spine configuration may evolve the rapid heating, and connectivity changes may occur due to the fragmentation via the K-H instability. It also act as a rapid mechanism to transfer the mass and energy release between two distinct regions separated by the fan-spine configuration.