Del. Fam. Ct. R. Civ. P. 62
(a) Stay on motion for new trial or for judgment. In its discretion and on such conditions for the security of the adverse party as are proper, the Court may stay the execution of or any proceedings to enforce a judgment pending the disposition of a motion for a new trial or to alter or amend a judgment made pursuant to Rule 59 or of a motion for relief from a judgment or order made pursuant to Rule 60.
(b) Injunction pending appeal. When an appeal is taken from an interlocutory or final judgment granting, dissolving, or denying an injunction, the Court in its discretion may suspend, modify, restore, or grant an injunction during the pendency of the appeal upon such terms as to bond or otherwise as it considers proper for the security of the rights of the adverse party.
(c) Supersedeas or stay on appeal. Stays pending appeal and stay and cost bonds shall be governed by Article IV, Section 24 of the Constitution of the State of Delaware and by the rules of the appellate court.
(d) Stay according to statute. A judgment debtor is entitled to a stay of execution where such stay is accorded by statute.
(e) Stay of judgment as to multiple claims or multiple parties. When a court has ordered a final judgment under the conditions stated in Rule 54(b), the Court may stay enforcement of that judgment until the entering of a subsequent judgment or judgments and may prescribe such conditions as are necessary to secure the benefit thereof to the party in whose favor the judgment is entered.
Del. Fam. Ct. R. Civ. P. 62