Using both DFT as well as G0W0 calculations, we investigate static and dynamic effects on the phosphorene band gap upon deposition and encapsulation on/in BN multilayers. We demonstrate how competing long- and short-range effects cause the phosphorene band gap to increase at low P-BN interlayer spacings, while the band gap is found to drop below that of isolated phosphorene in the BN/P bilayer at intermediate distances around 4 A. Subsequent stacking of BN layers, i.e., BN/BN/P and BN/BN/BN/P is found to have a negligible effect at the DFT level while at the G0W0 level, increased screening lowers the band gap as compared to the BN/P bilayer. Encapsulation between two BN layers, on the other hand, is found to further increase the phosphorene band gap with respect to the BN/P bilayer. Lastly we investigate the use of the GLLB-SC functional as a starting point for G0W0 calculations showing it to, in the case of phosphorene, yield results close to those obtained from GW0@PBE.