Clustering is a data mining activity that aims to differentiate groups inside a given set of objects, with respect to a set of relevant attributes of the analyzed objects. Generally, existing clustering methods start with a known set of objects, measured against a known set of attributes. But there are numerous applications where the attribute set characterizing the objects evolves. We propose in this paper an incremental clustering method based on an hierarchical agglomerative approach, Hierarchical Core Based Incremental Clustering (HCBIC), that is capable to re-partition the object set, when the attribute set increases. The method starts from the partitioning into clusters that was established by applying the hierarchical clustering algorithm (HCA) before the attribute set changed. The result is reached by HCBIC more efficiently than running HCA again from the scratch on the feature-extended object set. Experiments proving the method?s efficiency are reported.