Privacy protection has become increasingly crucial in the field of epilepsy prediction. Some latest studies introduced the source-free domain adaptation (SFDA), which only utilizes a pretrained source model for protecting the source data privacy. However, the existing SFDA methods exist two shortcomings: 1) the offline setting, which is not suitable for real-world online scenarios and 2) the poor performance, which is attributed to the absence of labeled calibration data during the adaptation phase. To this end, we proposed an online seizure prediction framework based on fine-tuning and test-time adaptation (FT3A). Specifically, FT3A employs one seizure event target data to fine-tune and continuously adapt the pretrained source model to unlabeled target data stream. In addition, the adaption and prediction is performed simultaneously. On the one hand, we design the task model as a multihead structure to increase the confidence of the model and reduce error accumulation. On the other hand, a memory bank is introduced to store a small amount of historical EEG data, which helps handle the catastrophic forgetting concern of the model during online adaptation. Extensive experiments on public CHB-MIT data set and the private Freiburg hospital data set indicate the superiority and generality of the proposed method.