A Grid could be a very dynamic environment and the user groups are highly diverse. A user group could be formed by the users of different domains with different infrastructures and managerial policies. Handling requests from a wide range of users from different domains becomes a challenge when attempting to accommodate all the differences. Service providers find it impossible to track all users in a Grid. Therefore, an access control mechanism that provides users appropriate access to the resources in a Grid is required. Role Based Access Control (RBAC) models have been demonstrated to be an effective and efficient approach to manage accesses in a computing system. Much has been done to adapt the RBAC concept to Grids and focus on the authorization and verification of the dynamic factors or contexts of a user. Some applications also allow administrators to change the policies during the authorization process, but they did not handle the authorization in real-time and on demand manner in a Grid. It is a critical authorization requirement for a Grid. Therefore, this problem motivated us to develop a new Dynamic Role Lease Authorization (DRLA) protocol for a Grid.