Fully connected Graph Transformers (GT) have rapidly become prominent in the static graph community as an alternative to Message-Passing models, which suffer from a lack of expressivity, oversquashing, and under-reaching.However, in a dynamic context, by interconnecting all nodes at multiple snapshots with self-attention,GT loose both structural and temporal information. In this work, we introduce Supra-LAplacian encoding for spatio-temporal TransformErs (SLATE), a new spatio-temporal encoding to leverage the GT architecture while keeping spatio-temporal information.Specifically, we transform Discrete Time Dynamic Graphs into multi-layer graphs and take advantage of the spectral properties of their associated supra-Laplacian matrix.Our second contribution explicitly model nodes' pairwise relationships with a cross-attention mechanism, providing an accurate edge representation for dynamic link prediction.SLATE outperforms numerous state-of-the-art methods based on Message-Passing Graph Neural Networks combined with recurrent models (e.g, LSTM), and Dynamic Graph Transformers,on~9 datasets. Code is open-source and available at this link https://github.com/ykrmm/SLATE.