The upgraded GMRT (uGMRT) with its unprecedented sensitivity and high figure of merit, is expected to result in the discovery of a large population of pulsars including pulsars of previously unknown type. In the phase-2 of the GMRT High Resolution Southern Sky (GHRSS) survey with the uGMRT we will reach 1/4th of sensitivity of the SKA Phase-1. In this paper we highlight the salient features of the survey of pulsars and fast transients with the uGMRT highlighting its discovery potential. The extended GMRT (eGMRT) equipped with wide field-of-view, increased collecting area will have unprecedented sensitivity in time-domain astronomy, reaching close to SKA-Phase1. Many fold increase in the number of elements, increase in the baseline length and addition of phased array feed will make eGMRT an excellent instrument for the survey of pulsars and transients with a promise of detecting large variety of pulsars and fast radio bursts.