In this paper, we focus on tracking the signal subspace under a sparsity constraint. More specifically, we propose a two-step approach to solve the considered problem whether the sparsity constraint is on the system weight matrix or on the source signals. The first step uses the OPAST algorithm for an adaptive extraction of an orthonormal basis of the principal subspace, then an estimation of the desired weight matrix is done in the second step, taking into account the sparsity constraint. The resulting algorithms: SS-OPAST and DS-OPAST have low computational complexity (suitable in the adaptive context) and they achieve both good convergence and estimation performance as illustrated by our simulation experiments for different application scenarios.