Short answer. Yes. When a court renders a separate judgment on one claim while the rest of the case continues, it may stay its enforcement until the rendition of a subsequent judgment or judgments, and it may also set conditions to protect the benefit of that judgment for the party who won it.
What the law says
the court by order may stay its enforcement until the rendition of a subsequent judgment or judgments and may prescribe such conditions as may be necessary to secure the benefit thereof to the party in whose favor the judgment is rendered
Rule 36, Section 5 — Separate judgments. Read the full provision →
How a separate judgment comes about
This tool exists for cases with more than one claim for relief. Once the issues material to one particular claim, and any counterclaims arising from the same transaction or occurrence, have been resolved, the court may render a separate judgment disposing of such claim. That judgment ends the action as to that specific claim, while the case continues forward on whatever claims remain, so the rule binds only the claim actually disposed of, not the parties' relationship on the rest of the case.
The stay is the court's choice, not automatic
Nothing in the rule makes enforcement of a separate judgment wait automatically. The rule gives the court discretion — by order — to stay enforcement until the remaining claims are decided. If the court does not issue such an order, the winning party can generally move to enforce the separate judgment on its own claim while the rest of the case is still pending, since the judgment already terminated the action as to that claim.
Why a court might choose to stay it anyway
A stay makes practical sense where enforcing one judgment early could complicate or prejudice how the remaining, related claims eventually get resolved — for instance, where money or property covered by the separate judgment could still be affected by what happens on the claims left pending. The rule leaves that balancing decision to the court handling the case, which is in the best position to weigh how the pending and decided claims relate to one another.
Protecting the winning party during the wait
A stay does not leave the party who won the separate judgment unprotected. The court may prescribe such conditions as may be necessary to secure the benefit thereof to the party in whose favor the judgment is rendered — conditions designed to make sure that whatever the separate judgment awarded is still available to that party once the stay eventually lifts — the rule does not leave that protection to chance, or to the losing party's cooperation.