Replaceable fuses as coupling elements, with detailed composite connections, can state the steel and concrete hybrid structures to be one of the best alternatives for a more feasible and easy repairable earthquake-proof structure. Therefore, an efficient composite connection for a newly suggested Hybrid Coupled Wall (HCW) system, consisting of a reinforced concrete shear wall coupled with steel side columns via dissipative steel shear links, is studied in this paper. The steel shear links are connected to a steel profile, embedded or passing through the RC wall. This embedded part should be so designed that the damage always occurs on the steel shear links (fuses) prior to minimal damage in the RC wall and embedded connection. The emphasis is on characterizing a suitable “steel link + embedded composite connection within the RC wall” configuration and calculate an appropriate embedment length while concentrating the seismic damage to the replaceable steel links. To this purpose, two joint configurations are designed through a capacity based approach, namely “partly embedded” and “passing through” steel beam connection and are examined through detailed FE analyses. A parametric study was also carried out to provide sufficient evidence towards the design considerations proposed in this study, in terms of strength, stiffness and bearing strength within the embedded connection.