A novel peer-to-peer (P2P) market design is proposed in this work for the distribution grid level. Envisioning that the grid constraints violations are the major challenge for P2P energy sharing, we propose these to be handled through the ancillary service (AS) market. By calculating the decomposable distribution locational marginal prices (DLMPs), the essential price signals of procuring ASs can be recovered to determine the grid usage prices (GUPs) to each P2P transaction. Hence, the GUPs, due to their decomposable properties, act as incentive signals for the P2P market to support the grid operation in terms of loss reduction, voltage support and congestion management. The proposed market design comprises i) an interactive market design of P2P trade & AS and, ii) a fully distributed peer-centric market-clearing model for P2P energy trade. The duality analysis provides the composition of market equilibrium prices of P2P trading and their interpretations. The case studies demonstrate the effectiveness of the proposed P2P trade to support grid operational objectives.