This work showcases the feasibility of vertically stacked nanosheet FET (NSFET) for charge trapping-based synapse for neuromorphic applications. The calibrated simulation models mimic the long-term potentiation (LTP) and depression (LTD) of biological synapses. Use of stacked nanosheet device facilitates a dense memory with high current. The work also evaluates the effect of number of pulses for LTP and LTD on the image classification accuracy of the MNIST dataset. The neural network results show high linearity, conductance, and symmetric behavior between LTP and LTD that aids achieves $\sim94.75$ % accuracy in image classification.