The previous Memorandum of Understanding (MoU) expired at midnight on Friday with no sign of a deal in place, leaving around 230 leading cricketers without contracts and the fate of future tours in limbo.
Once the deadline passed, Australia's players threatened to boycott an "A" team tour of South Africa later this month unless a new agreement was struck with Cricket Australia beforehand.
"What needs to happen is keep the current MoU for the next 12 months and allow the players to get back to what they do best," Clarke told reporters at Nine Network's marketing launch for the Ashes.
"Cricket Australia, the ACA (Australian Cricketers' Association), please go behind closed doors and sort this in private.
"The players want to play... let's allow them to play while this stuff gets sorted out in the background."
At the heart of the acrimonious dispute is Cricket Australia's (CA) insistence that the two-decade-old model, under which players get a fixed percentage of revenue, should be jettisoned.
CA believes the revenue-share model is unfit for modern times and is starving grass-roots cricket of funding, while players say it has underpinned the game's growth and prosperity over the past 20 years.
"I don't want the Australian players to be unprepared because they have been concentrating on something else; give them 12 months and let them concentrate on the cricket," Clarke said. "I don't want to see any cricket missed.
"There will be a compromise. The ACA and Cricket Australia will find a way to make this work."
The ACA has called on CA chief executive James Sutherland to come to the negotiating table but he has remained silent since emailing players in May, informing them they would be unemployed if they failed to agree to a new MoU by the June 30 deadline.
"It does seem very strange. You've got to wonder what the hell is going on," former Australia captain Ian Chappell said.
"They've done a few strange things and Sutherland not being involved is one of them.
"I don't see a really good reason for him not to be."
Further tournaments, including a two-test tour of Bangladesh and a one-day international series in India also remain in doubt if the dispute continues to linger on.
"I can't believe they (CA) will want to upset India, so I would have thought that something will happen before," he said.
"Because they won't want to cancel that. If they get something done then, people will have probably forgotten by (the time the Ashes start in) November."
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
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