The 30-year-old may have a more important role than anyone at the club under his new manager.
But, before he can impose his style at Anfield when it comes to going forward, he absolutely has to sort out his new club's flailing back four.
Under Brendan Rodgers, the one criticism that can't be denied in any way is that Liverpool's defence was abysmal for over three seasons.
Unlike the defensive solidity Rafa Benitez was revered for, Rodgers struggled to get anything out of his back four even when the Reds came close to winning the Premier League title. Had they actually had a defence to speak of, their attack could have won that league at a canter...
That's why Klopp's tenure needs to ensure defensive progression. And that's why Martin Skrtel will be so important.
At 30, he is Liverpool's most senior and experienced defender (Kolo Toure is older but has spent less time on Merseyside and isn't a starter). Technically, though, the Slovakian isn't the greatest. He is sheer brute strength & determination at times and he needs to lead from the back and really solidify things at Anfield.
Alongside him, Dejan Lovren has underperformed criminally, while Mamadou Sakho has also been very shaky in key areas since moving to Merseyside.
If Skrtel can get things right for himself first and foremost, he can then help his fellow centre-backs settle into a rhythm under Klopp.
No one may be as central to the Liverpool line-up as Skrtel. Daniel Sturridge is key but is always a fitness concern. Christian Benteke, Danny Ings, Philippe Coutinho, Roberto Firmino and more all face heavy competition up front. James Milner may be utilised in different positions and Jordan Henderson is currently out injured. Even Simon Mignolet is very droppable.
We all know who Klopp brought the best out of at Borussia Dortmund in Neven Subotic and Mats Hummels. And, if Liverpool are to be successful under the German, Skrtel needs to become his new go-to centre-back.