Interfering sources, background noise and reverberation degrade speech quality and intelligibility in hearing aid applications. In this paper, we present an adaptive algorithm aiming at dereverberation, noise and interferer reduction and preservation of binaural cues based on the wBLCMP beamformer. The wBLCMP beamformer unifies the multi-channel weighted prediction error method performing dereverberation and the linearly constrained minimum power beamformer performing noise and interferer reduction into a single convolutional beamformer. We propose to adaptively compute the optimal filter by incorporating an exponential window into a sparsity-promoting lp-norm cost function, which enables to track a moving target speaker. Simulation results with successive target speakers at different positions show that the proposed adaptive version of the wBLCMP beamformer outperforms a non-adaptive version in terms of objective speech enhancement performance measures.