Interesting that Liverpool fans say Virgil over Suarez - I get that VVD was the lynchpin of a UCL winner while Suarez didn't win anything at Liverpool, but Suarez's 2013-14 is IMO the greatest individual season in EPL history AND I don't think Klopp-era Liverpool and all the accompanying success happens without Suarez's time there.
For Chelsea, Nemanja Matic jumps to mind. I have fond, fond memories of Chelsea-Man City in Jan/Feb 2014 (I think it was his first game for us, but I could be misremembering) and him and David Luiz (another January signing, FWIW) absolutely bossing the midfield.
Funnily enough, given what just happened this month, Chelsea have been quiet in January for the past bunch of years. This insane spending spree has been our first January signings since we brought in Giroud, Emerson, and Barkley in 2018 (I'm not counting Pulisic in 2019 because he didn't join until the summer).
EDIT: looked it up, it was Matic's first start, not his first game.