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.
Les Mielles golf course up for sale
Youngest politician is first guest on new Channel 103 show
Call for urgency on any Jersey under-16 social media ban
Jersey teen 'shocked' at winning music competition
Under-16 social media ban 'will protect children'
Hospital air-con failure fixed
Jersey Zoo welcomes baby cabybaras
Parish officially takes over Sandy Park
