The performance of the gas turbine engines deteriorates under off-design conditions with the change of required power demand. The performance of the engine can be improved by actively controlling the mass flow rate through the engine turbine section using the variable area nozzle turbine (VANT). However, to implement VANT, vanes of the turbine nozzle need to be rotated, which demands part clearance to be provided near both the hub and tip region. In order to keep constant part clearance during vane turning, endwalls are modified to spherical shapes in such a way that distance between vane and upstream as well downstream rotor remains unaffected. Also, vanes are rotated about its pivot, which creates a blockage to the leakage flow in the part clearance. As pivot creates a blockage to the leakage flow, the shape of the pivot need to be selected in such a way that leakage losses can be reduced effectively. Hence, to analyze the effect of different pivot shapes on leakage losses, two different shapes of the pivot i.e., circular and elliptic, are explored in the present study. Also, three vane turning angles are analyzed to observe the effectiveness of these pivot shapes. The effect of the pivot is analyzed by entropy contours and total pressure loss coefficient in the exit plane, and it is found that the elliptic pivot performs better than a circular pivot as an elliptic pivot provides more blockage to the leakage flow and hence minimizing the overall losses.