We perform atomistic simulations aimed on study of diffusion of constituents and niobium precipitation in hcp Zr-Nb. We report diffusivities of Zr and Nb in hcp Zr-Nb alloys computed for the models containing up to 5 at.% of niobium. The calculated diffusivity of niobium rises with increase of its content in the alloy. The simulations also show that for a studied concentration range addition of niobium slightly enhances self-diffusion of zirconium in the alloys. The work is also devoted to description of niobium incorporation and clusterization in hcp zirconium. It is confirmed that for a single niobium atom incorporated in hcp zirconium lattice the octahedral position is the most favorable. We estimated the energy describing niobium cluster formation in pure hcp zirconium. According to the simulation results, we can suggest that the minimum niobium cluster size that can be expected in hcp Zr corresponds to about 80 atoms.