Incorporating new business and trading models in the process of hosting capacity (HC) analyses of distribution systems is of great importance. Accordingly, this paper presents a two-stage methodology to investigate the effects of flexibility contracts (FlexCons) on the HC assessment of distribution grids. In the first stage, the maximization of FlexCon exchanges between photovoltaic (PV) solar owners and demands is addressed. In the second stage, an optimization-based HC calculation is carried out for various cases with and without considering FlexCons. In particular, the impacts of location and number of FlexCons on the HC are studied. The results of simulations on a 33-bus radial distribution network indicate an increase in PV-HC by considering contract-based trading of power flexibility through FlexCons.