Wakefield have lifted the suspension on two of the four players stood down a week ago pending the outcome of internal investigations.
Forward Scott Anderson and threequarter Reece Lyne resumed training on Wednesday and look set to return to the Wildcats team for Sunday's final match of the Super 8s Qualifiers against Sheffield Eagles at Bramall Lane.
Full-back Kevin Locke and scrum-half Tim Smith remain suspended and the subject of a police investigation into a car crash in Hull 10 days ago.
Lyne was also thought to have been involved in that incident but it is understood he played only a minor role while Anderson's disciplinary issue was unconnected.
Smith has been bailed to appear before magistrates later this month charged with driving without due care and attention.
Meanwhile, Carter says he is confident the club will still be playing at their historic Belle Vue home next season after successfully re-negotiating a rent reduction.
Carter had threatened to move the club out of the ground because of the high costs and had lined up a temporary ground-share with Championship club Dewsbury for 2016 if talks with owners Bank of Ireland failed to resolve the impasse.
"We've got agreement in principle to carry on using the ground," Carter said.
"We have to firm things up but I don't see any obstacles.
Carter says alternative plans to develop Belle Vue, which is one of only five grounds still in use from the time of the breakaway from the Rugby Football Union in 1895, were impractical.
"It became more difficult," he said. "It's an old facility."
Belle Vue will be full to the rafters on Saturday week if they beat Sheffield on Sunday to earn home advantage against Bradford in the Million-Pound Match to determine the 12th and final place in Super League for 2016.
In 2006, 11,000 people crammed into the ground to watch Wakefield beat Castleford in their promotion decider but the current ground capacity is expected to be confirmed at just short of 8,000.