Inclusion dependencies form one of the most fundamental classes of integrity constraints. Their importance in classical data management is reinforced by modern applications such as data profiling, data cleaning, entity resolution and schema matching. Their discovery in an unknown dataset is at the core of any data analysis effort. Therefore, several research approaches have focused on their efficient discovery in a given, static dataset. However, none of these approaches are appropriate for applications on dynamic datasets, such as transactional datasets, scientific applications, and social network. In these cases, discovery techniques should be able to efficiently update the inclusion dependencies after an update in the dataset, without reprocessing the entire dataset. We present the first approach for incrementally updating the unary inclusion dependencies. In particular, our approach is based on the concept of attribute clustering from which the unary inclusion dependencies are efficiently derivable. We incrementally update the clusters after each update of the dataset. Updating the clusters does not need to access the dataset because of special data structures designed to efficiently support the updating process. We perform an exhaustive analysis of our approach by applying it to large datasets with several hundred attributes and more than 116,200,000 million tuples. The results show that the incremental discovery significantly reduces the runtime needed by the static discovery. This reduction in the runtime is up to 99.9996 % for both the insert and the delete.