They face Championship rivals Featherstone Rovers there in the 1895 Cup final on Saturday, knowing they face a significant challenge to cause an upset.
York are on a six-game losing run while, in contrast, their unbeaten rivals have won all 12 of their league games this term.
Clarkson played for Leeds Rhinos in the 2010 Challenge Cup final, just a couple of weeks after quitting his job as a bricklayer having made a late rise into his hometown club’s first team.
However, Leeds lost to Warrington Wolves and he was a Wembley runner-up again 12 months later against Wigan Warriors while, when they did finally lift the Cup against Castleford Tigers in 2014, Clarkson did not make the matchday squad.
Asked if there was unfinished business for him, the 31-year-old said: “I suppose there is.
“I’ve been there a couple of times (and lost) and been in the squad when Leeds have won it but not been on the field.
“It was upsetting (in 2014) but the day itself was amazing. You have to enjoy the occasion whether you’re in the squad or playing.
“And it’d be absolutely fantastic to win a final there now.
“My family is going down, the missus and the kids, and my mum and dad, so it’d be nice to win it in front of them as well.”
York do have a lot of players with Wembley experience in their ranks, including former England centre Ryan Atkins who was in the Warrington side in 2010 and Danny Washbrook, who lifted the trophy twice with Hull FC. But former Hull KR back-row Clarkson, who joined York from Castleford Tigers last season, knows they all have to quickly find some form.
He said: “In a week, there’s not a lot you can change as a team. It’s a mentality thing at the minute, I think.
“We’re struggling. We’re in bit of a rut but there’s only us who can get ourselves out of it.
“We’ll most likely prepare well as a team but it’s as individuals we have to prepare well for as well and take the occasion out of it, enjoy it down there but focus on the job at hand.”
Meanwhile, Thursday’s derby between Hull KR and Hull FC is off for a second time as Hull have more than seven players unavailable for Covid-related reasons.
Hull KR’s Under-16s coach Ben Cockayne has left the club by mutual consent. He was fined £2,000 last week for repeated breaches of the RFL’s social media, safeguarding and Covid-19 policies.