Reliable uncertainty quantification is essential in survival prediction, particularly in clinical settings where erroneous decisions carry high risk. Conformal prediction has attracted substantial attention as it offers a model-agnostic framework with finite-sample coverage guarantees. Extending it to right-censored outcomes poses nontrivial challenges. Several adaptations of conformal approaches for survival outcomes have been developed, but they either rely on restrictive censoring settings or substantial computation. A recent conformal approach for right-censored data constructs censoring-adjusted p-values and enables prediction intervals in general survival settings. However, the empirical coverage depends sensitively on heuristic tuning choices and its validity is limited to scenarios without covariate shift. In this paper, we establish theoretical justification for its prediction-set construction, providing a principled basis for defining prediction-set bounds, and extend the approach to covariate-shift settings. Simulation studies and a real data application demonstrate that the proposed method achieves robust coverage and coherent interval structure across varying censoring levels and covariate-shift settings.

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