Small area estimation is an important tool to produce estimates of poverty for regions with low or zero sample sizes. Estimates are typically obtained by combining a consumption survey reporting on poverty and a census providing the spatial disaggregation. This paper discusses an updating method that produces up‐to‐date small area estimates when only a dated census and a more recent survey are available and predictors are subject to drift over time, a situation commonly encountered in practice. Instead of using survey variables to explain consumption in the survey, the updating approach uses only variables constructed from the census. The proposed estimator has fewer data requirements and weaker assumptions than common small area estimators. Applications to simulated data and to poverty estimation in Brazil show an overall good performance, but also imply the importance of examining practical challenges in real‐world applications.