Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the distribution of normality can be changed due to the distribution shifts between training and test data. This paper highlights the prevalence of the new normal problem in unsupervised time-series anomaly detection studies. To tackle this issue, we propose a simple yet effective test-time adaptation strategy based on trend estimation and a self-supervised approach to learning new normalities during inference. Extensive experiments on real-world benchmarks demonstrate that incorporating the proposed strategy into the anomaly detector consistently improves the model's performance compared to the baselines, leading to robustness to the distribution shifts.