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Predicting risks of chronic diseases has become increasingly important in clinical practice. When a prediction model is developed in a given source cohort, there is often a great interest to apply the model to other cohorts. However, due to potential discrepancy in baseline disease incidences between different cohorts and shifts in patient composition, the risk predicted by the original model often under- or over-estimates the risk in the new cohort. The remedy of such a poorly calibrated prediction is needed for proper medical decision-making. In this article, we assume the relative risks of predictors are the same between the two cohorts, and propose a novel weighted estimating equation approach to re-calibrating the projected risk for the targeted population through updating the baseline risk. The recalibration leverages the knowledge about the overall survival probabilities for the disease of interest and competing events, and the summary information of risk factors from the targeted population. The proposed re-calibrated risk estimators gain efficiency if the risk factor distributions are the same for both the source and target cohorts, and are robust with little bias if they differ. We establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation studies demonstrate that the proposed estimators perform very well in terms of robustness and efficiency in finite samples. A real data application to colorectal cancer risk prediction also illustrates that the proposed method can be used in practice for model recalibration.