We investigate the settling hydrodynamics of a sphere confined along the centerline of a square tube filled with active nematic fluid. The sphere is restricted from rotation and subjected to either planar or homeotropic anchoring conditions on its surface. Our study focuses on the regime where direct active forces exerted on the sphere are much weaker than the hydrodynamic or chemical forces. We find that activity can still significantly alter the settling velocity by modifying the flow structure and nematic field. We first examine the fundamental settling behavior in the absence of activity, where the sphere's velocity varies nonmonotonically with the elastic constant ($K$) but increases with the collective rotational diffusion constant (Г). Introducing activity by activity number (${\tilde{K}}^{-1/2}$) while fixing $K=0.05$, $\mathrm{\Gamma }=0.5$, and Galileo number $\left(\text{Ga}\right)=5.0$, we observe that the axisymmetric flow structure emerges at low ${\tilde{K}}^{-1/2}$, where the extensile activity squeezes the vortex and enhances settling, whereas the contractile activity expands the vortex and suppresses settling. In addition, active nematics can alter the “effective viscosity” of the local flow, which in turn affects the settling velocity. As activity increases, we found that transitions between distinct flow patterns also play a critical role in altering the settling velocity. Specifically, the flow with nonzero helicity emerges at moderate activity in extensile fluids and leads to an abrupt reduction in the sphere's settling velocity. This reduction is related to the transition in the flow pattern and a corresponding shift in the deformation of the nematic field from bend to twist. The effect is particularly pronounced with homeotropic anchoring owing to the stronger helicity of the flow.

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