The detection of new multiple sclerosis (MS) lesions is an important marker of the evolution of the disease. The applicability of learning-based methods could automate this task efficiently. However, the lack of annotated longitudinal data with new-appearing lesions is a limiting factor for the training of robust and generalizing models. In this study, we describe a deep-learning-based pipeline addressing the challenging task of detecting and segmenting new MS lesions. First, we propose to use transfer-learning from a model trained on a segmentation task using single time-points. Therefore, we exploit knowledge from an easier task and for which more annotated datasets are available. Second, we propose a data synthesis strategy to generate realistic longitudinal time-points with new lesions using single time-point scans. In this way, we pretrain our detection model on large synthetic annotated datasets. Finally, we use a data-augmentation technique designed to simulate data diversity in MRI. By doing that, we increase the size of the available small annotated longitudinal datasets. Our ablation study showed that each contribution lead to an enhancement of the segmentation accuracy. Using the proposed pipeline, we obtained the best score for the segmentation and the detection of new MS lesions in the MSSEG2 MICCAI challenge.