Spectrum sharing is a promising solution for the problem of spectrum congestion. We consider a spectrum sharing scenario between a multiple-input multiple-output (MIMO) radar and Long Term Evolution (LTE) Advanced cellular system. In this paper, we consider resource allocation optimization problem with carrier aggregation. The LTE Advanced system has N _BS base stations (BS) which it operates in the radar band on a sharing basis. Our objective is to allocate resources from the LTE Advanced carrier and the MIMO radar carrier to each user equipment (UE) in an LTE Advanced cell based on the running application of UE. Each user application is assigned a utility function based on the type of application. We propose a carrier aggregation resource allocation algorithm to allocate the LTE Advanced and the radar carriers' resources optimally among users based on the type of user application. The algorithm gives priority to users running inelastic traffic when allocating resources. Finally we present simulation results on the performance of the proposed carrier aggregation resource allocation algorithm.