Can you provide a bit more context as to what you are attempting to do? It is indeed the case that Dirichlet boundary conditions restrict the test space in that sense (this is often referred to as "lifting" the boundary conditions). However it's not generally possible to lift the component of a vector field normal to the boundary (because this does not directly correspond to a particular set of degrees of freedom), so if you can provide a little more context about the problem, we may be able to provide a suitable alternative.