Deputy Steve Ahier will be put forward for the role of Infrastructure Minister following the resignation of Deputy Tom Binet.
His sister, Deputy Rose Binet also left her role as Assistant Health Minister before co-signing the motion.
St Clement Constable Marcus Troy has taken her position.
The States will vote on the appointment of a new Infrastructure Minister when they sit on 16 January and if the Chief Minister survives the confidence vote.
Deputy Steve Ahier is who she wants to fill the role, but any other States Members can put themselves forward for it.
The party's ten votes could be what swings the vote in either direction.
The Chief Minister says she will take up the portfolio left behind by Deputy Binet until politicians can vote in a new minister.
Deputy Lucy Stephenson and Deputy Ahier will take the role of assistant ministers during that time as well.
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