Multimedia and delay-sensitive data applications in cognitive radio sensor networks (CRSN) require efficient real-time communication and dynamic spectrum access (DSA) capabilities. This requirement poses emerging problems to be addressed in inherently resource-constrained sensor networks, and needs investigation of CRSN challenges with real-time communication requirements. In this paper, the main design challenges and principles for multimedia and delay-sensitive data transport in CRSN are introduced. The existing transport protocols and algorithms devised for cognitive radio ad hoc networks and wireless sensor networks (WSN) are explored from the perspective of CRSN paradigm. Specifically, the challenges for real-time transport in CRSN are investigated in different spectrum environments of smart grid, e.g., 500kV substation, main power room and underground network transformer vaults. Open research issues for the realization of energy-efficient and real-time transport in CRSN are also presented. Overall, the performance evaluations provide valuable insights about real-time transport in CRSN and guide design decisions and trade-offs for CRSN applications in smart electric power grid.