In this article, we report an evidence of very high and statistically significant relationship between hemispheric asymmetry in solar coronal rotation rate and solar activity. Our approach is based on cross correlation of hemispheric asymmetry index (AI) in rotation rate with annual solar activity indicators. To obtain hemispheric asymmetry in solar rotation rate, we use solar full disc (SFD) images at 30.4 nm, 19.5 nm, and 28.4 nm wavelengths for 24th Solar Cycle i.e., for the period from 2008 to 2018, as recorded by the Solar Terrestrial Relations Observatory (STEREO) space mission. Our analysis shows that hemispheric asymmetry in rotation rate is high during the solar maxima from 2011 to 2014. On the other hand, hemispheric asymmetry drops gradually on both sides (i.e., from 2008 to 2011 and from 2014 to 2018). The results show that asymmetry index (AI) leads sunspot numbers by ~1.56 years. This gives a clear indication that hemispheric asymmetry triggers the formation of sunspots working together with the differential rotation of the Sun.