Haw. Rev. Stat. § 634J-2
In any litigation pending in any court of this State, at any time until final judgment is entered, a defendant may move the court, upon notice and hearing, for an order requiring the plaintiff to furnish security. The motion must be based upon the ground, and supported by a showing, that the plaintiff is a vexatious litigant and that there is no reasonable probability that the plaintiff will prevail in the litigation against the moving defendant.
HRS § 634J-2
As matters under this section are not exceptional matters, while a family court case (including an independent action) is on appeal, the family court has no jurisdiction to act in the case on appeal pursuant to this chapter absent prior permission by the appellate court having jurisdiction over the appeal. 97 H. 340 (App.), 37 P.3d 589.