Here we study the new concept of restrained isolate edge geodetic set for a graph of order $n$. The edge geodetic set of a connected graph is said to be a restrained isolate edge geodetic set if the induced subgraph has at least one isolate vertex and the induced subgraph has no isolate vertex. The restrained isolate edge geodetic number denoted by $g_{rie}(G)$ is the minimum cardinality of a restrained isolate edge geodetic set of $G$. Here we determine the restrained isolate edge geodetic number of some standard graphs and by adding leaf vertices to a graph $G$. In addition, we determine the restrained isolate edge geodetic number for some graphs using cartesian product and corona product.