NaFeAs belongs to a class of Fe-based superconductors which have parent compounds that show separated structural and magnetic transitions. Effects of the structural transition on spin dynamics therefore can be investigated separately from the magnetic transition. A plateau in dynamic spin response is observed in a critical region around the structural transition temperature T S. It is interpreted as being due to the stiffening of spin fluctuations along the in-plane magnetic hard axis due to the d xz and d yz orbital ordering. The appearance of anisotropic spin dynamics in the critical region above the T S at T (*) offers a dynamic magnetic scattering mechanism for anisotropic electronic properties in the commonly referred 'nematic phase'.