Randomized trials with limited concurrent control information---including but not limited to unequal-randomization settings---can offer ethical and practical advantages, especially in pediatric and rare diseases, but they often lose power because fewer control patients are available for direct comparison. Borrowing information from external controls may improve efficiency, but can also inflate the Type I error rate when the external and trial populations are not sufficiently comparable. We propose RECaST-Surv, a Bayesian transfer-learning framework for time-to-event outcomes that extends the RECaST method to survival settings. The method learns a structural survival model from external control data and calibrates it to the concurrent control arm of the current trial through a Cauchy random effect. To improve frequentist operating characteristics, we further develop a bootstrap-based procedure to calibrate the testing rule for Type I error control. RECaST-Surv can accommodate multiple external datasets and requires only summary-level information from external sources. Simulation studies show that the method maintains near-nominal Type I error across challenging settings while improving power by roughly 10%--12% over standard analyses. In an Amyotrophic Lateral Sclerosis trial emulation, RECaST-Surv increased power from 82.8% to 95.7% relative to the no-borrowing RCT analysis, while maintaining acceptable error control.

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