Dynamic spectrum access (DSA) is a challenging issue among the cognitive radio (CR) users. In this paper, we investigate an interference-aware local cartography-based DSA (LC-DSA) technique for OFDM-based CR system. In particular, a joint power and frequency resource block (RB) allocation technique has been proposed for resource allocation among secondary users (SUE) exploiting radio environmental map (REM) of the local surrounding environment. With REM, we produce an interference database for each RB at each SUE's location. Having knowledge of these measured interference values, LC-DSA technique elaborates an interference cartography (IC) diagram of CR coverage area with the help of spatial interpolation algorithm. Using IC diagram, CR applies interference classification algorithm to classify RBs at target location and uses them for transmission with appropriate transmit power without producing interference above the threshold value to the primary user (PUE). Our simulation results show how the proposed LC-DSA technique significantly improves the system throughput. Simultaneously, the interference introduced to the PUE remains within a tolerable limit.