This paper presents a new-partial adaptive space-time filtering technique for clutter and/or jammer suppression in phased array radar systems. In this work, two proposed filter configurations are considered. These filters utilize a rectangular phased array antenna (two-dimension) with "NxNy" sensors as an adaptive space-time signal-processing unit. The first configuration is referred to as fully adaptive space-time filter "FASTF", and the second configuration is referred to as partially adaptive space-time filter "PASTE'. A computer code has been developed on MATLAB-R12 to simulate the operation processes of both filters as well as the signal and interference environment. The objective is to analyze, investigate and evaluate the performance of the new-presented partial adaptive filter versus the full adaptive one in case of search and tracking radar systems. Results of simulation indicate that the new-partially adaptive filter has a good performance (output signal to interference plus noise ratio or improvement factor) as close as to the full adaptive filter for the same interference conditions. In addition, partially adaptive filter is less complex than the first filter's configuration. Also, a tremendous reduction in the overall processing time has been achieved using the partially adaptive filter's configuration.