We are conducting a survey for pulsars and transients using the Giant Metrewave Radio Telescope (GMRT). The GMRT High Resolution Southern Sky (GHRSS) survey is an off-Galactic-plane (|b|>5) survey in the declination range -40 deg to -54 deg at 322 MHz. With the high time (up to 30.72 micro-sec) and frequency (up to 0.016275 MHz) resolution observing modes, the 5-sigma detection limit is 0.5 mJy for a 2 ms pulsar with 10% duty cycle at 322 MHz. Total GHRSS sky coverage of 2866 square-deg, will result from 1953 pointing, each covering 1.8 square-deg. The 10-sigma detection limit for a 5 milli-sec transient burst is 1.6 Jy for the GHRSS survey. In addition, the GHRSS survey can reveal transient events like rotating radio transients or fast radio bursts. With 35% of the survey completed (i.e. 1000 square-deg), we report the discovery of 10 pulsars, one of which is a millisecond pulsar (MSP), one of the highest pulsar per square degree discovery rates for any off-Galactic plane survey. We re-detected 23 known in-beam pulsars. Utilising the imaging capability of the GMRT we also localised 4 of the GHRSS pulsars (including the MSP) in the gated image plane within +/- 10 arc-second. We demonstrated rapid convergence in pulsar timing with a more precise position than is possible with single dish discoveries. We also exhibited that we can localise the brightest transient sources with simultaneously obtained lower time resolution imaging data, demonstrating a technique that may have application in the SKA.