Efficient estimation of population parameters in small area estimation (SAE) is crucial, especially under stratified random sampling when nonresponse occurs. Several estimators have been developed to improve estimation accuracy. However, some of these methods often fail to fully adjust for nonresponse bias, leading to unreliable domain mean estimates. This study proposes a new calibration-based estimator, by integrating the Kullback-Leibler distance function-based weight adjustments. The estimator is formulated under two conditions: when nonresponse affects only the study variable, and when nonresponse affects both study and auxiliary variables. Properties of the estimators have been derived and the results confirm that the proposed estimator provides greater efficiency and lower error rates than existing methods. Empirical validation is conducted using data from a longitudinal survey (before, during, and after COVID-19) from Household Finance & Consumption Survey (HFCS) and Integrated Household Survey (IHS) for 2019-2021 from the Department of Statistic of the Central Bank of Nigeria. Comparative performance analysis using variance and mean square error calculations demonstrates that the proposed estimator consistently outperforms the existing domain estimators in handling nonresponse across different domains. The study concludes that calibration techniques enhance estimation accuracy in stratified sampling and offers recommendations for further research on alternative calibration functions in small area estimation.