Transformer-based sequential recommendation (SR) models excel at modeling long-range dependencies, but suffer from high computational costs and catastrophic forgetting during continuous updates. Although continual learning has been applied to recommendation, existing methods gradually forget long-term user preferences and remain underexplored in SR. In this paper, we introduce Continual Sequential Transformer for Recommendation (CSTRec), which effectively adapt to current interests by leveraging preserved historical knowledge. Its core is Continual Sequential Attention (CSA), a linear attention tailored for continual SR, which partially retain historical knowledge without direct access to prior data. CSA features: (1) Cauchy-Schwarz Normalization to stabilize learning over time under uneven user interaction frequencies, and (2) Collaborative Interest Enrichment via shared, learnable interest pools to mitigate forgetting. We also introduce a new technique for new user adaptation by transferring historical knowledge from existing users with similar interests. Extensive experiments show CSTRec's superior performance in both knowledge retention and acquisition. Our code is available at https://github.com/Gyu-Seok0/CSTRec_WSDM26.