In the field of speaker verification, session or channel variability poses a significant challenge. While many contemporary methods aim to disentangle session information from speaker embeddings, we introduce a novel approach using an additional embedding to represent the session information. This is achieved by training an auxiliary network appended to the speaker embedding extractor which remains fixed in this training process. This results in two similarity scores: one for the speakers information and one for the session information. The latter score acts as a compensator for the former that might be skewed due to session variations. Our extensive experiments demonstrate that session information can be effectively compensated without retraining of the embedding extractor.