Traffic accident prediction is a crucial task in the mobility domain. State-of-the-art accident prediction approaches are based on static and uniform grid-based geospatial aggregations, limiting their capability for fine-grained predictions. This property becomes particularly problematic in more complex regions such as city centers. In such regions, a grid cell can contain subregions with different properties; furthermore, an actual accident-prone region can be split across grid cells arbitrarily. This paper proposes Adaptive Clustering Accident Prediction (ACAP) - a novel accident prediction method based on a grid growing algorithm. ACAP applies adaptive clustering to the observed geospatial accident distribution and performs embeddings of temporal, accident-related, and regional features to increase prediction accuracy. We demonstrate the effectiveness of the proposed ACAP method using open real-world accident datasets from three cities in Germany. We demonstrate that ACAP improves the accident prediction performance for complex regions by 2-3 percent points in F1-score by adapting the geospatial aggregation to the distribution of the underlying spatio-temporal events. Our grid growing approach outperforms the clustering-based baselines by four percent points in terms of F1-score on average.