Robots and autonomous vehicles should be aware of what happens in their surroundings. The segmentation and tracking of moving objects are essential for reliable path planning, including collision avoidance. We investigate this estimation task for vehicles using radar sensing. We address moving instance tracking in sparse radar point clouds to enhance scene interpretation. We propose a learning-based radar tracker incorporating temporal offset predictions to enable direct center-based association and enhance segmentation performance by including additional motion cues. We implement attention-based tracking for sparse radar scans to include appearance features and enhance performance. The final association combines geometric and appearance features to overcome the limitations of center-based tracking to associate instances reliably. Our approach shows an improved performance on the moving instance tracking benchmark of the RadarScenes dataset compared to the current state of the art.