We report the discovery of NGTS-11 b ( =TOI-1847 b ) , a transiting Saturn in a 35.46 -day orbit around a mid K-type star ( T _ { eff } = 5050 \pm 80 K ) . We initially identified the system from a single-transit event in a TESS full-frame image light-curve . Following seventy-nine nights of photometric monitoring with an NGTS telescope , we observed a second full transit of NGTS-11 b approximately one year after the TESS single-transit event . The NGTS transit confirmed the parameters of the transit signal and restricted the orbital period to a set of 13 discrete periods . We combined our transit detections with precise radial velocity measurements to determine the true orbital period and measure the mass of the planet . We find NGTS-11 b has a radius of 0.817 \pm _ { 0.032 } ^ { 0.028 } R _ { Jup } , a mass of 0.344 \pm _ { 0.073 } ^ { 0.092 } M _ { Jup } , and an equilibrium temperature of just 435 \pm _ { 32 } ^ { 34 } K , making it one of the coolest known transiting gas giants . NGTS-11 b is the first exoplanet to be discovered after being initially identified as a TESS single-transit event , and its discovery highlights the power of intense photometric monitoring in recovering longer-period transiting exoplanets from single-transit events .