The application workloads in the modern multicore platform are becoming increasingly dynamic. It becomes challenging when multiple applications need to be executed in parallel in such systems. Mapping and scheduling of these applications are critical for system performance, and energy consumption, especially in Network-on- Chip (NoC) based multicore systems. These systems with multitasking processors offer a better opportunity for parallel application execution. Mapping solutions generated at design-time may be inappropriate for dynamic workloads. To improve the utilization of the underlying multicore platform and cope with the dynamism of application workload, often, task allocation is carried out dynamically. This paper presents a hybrid task allocation and scheduling strategy which exploits the design-time results at run-time. By considering the multitasking capability of the processors, communication energy and timing characteristics of the tasks, different allocation options are obtained at design-time. During run-time, based on the availability of the platform resources and application requirements, the design-time allocations are adapted for mapping and scheduling of tasks which result in improved run-time performance. Experimental results demonstrate that the proposed approach achieves, on an average 11.5%, 22.3%, 28.6% and 34.6% reduction in communication energy consumption as compared to CAM , DEAMS , TSMM  and CPNN , respectively for NoC based multicore platforms with multitasking processors. Also, the deadline satisfaction of the tasks of allocated applications improves on an average by 32.8% when compared with the state-of-the-art dynamic resource allocation approaches.