This paper presents a safe active learning approach for time-series modeling using Gaussian processes (GPs). The method addresses the challenge of learning time-series models while ensuring safety constraints are respected. The approach dynamically explores the input space to generate informative input and output trajectories for model learning. The input trajectory is parametrized into consecutive sections, which are determined stepwise based on safety requirements and past observations. A Gaussian process is used to model the time-series function, while another GP is employed to predict safe input regions. The algorithm solves a constraint optimization problem to determine input trajectory sections, taking safety predictions into account. The main contributions of the paper are: (1) Formulating an active learning setting for time-series models with dynamic exploration within the GP framework. (2) Incorporating the safety aspect into the exploration mechanism and deriving an appropriate criterion for dynamic input space exploration. (3) Providing a theoretical analysis of the algorithm and empirically evaluating the proposed approach on a realistic technical use case. The paper evaluates the approach on synthetic data and a real-world high-pressure fluid system. The results show that the method effectively learns time-series models while respecting safety constraints. The algorithm is shown to improve model approximation and safely explore the input space, with the ability to adjust the safety threshold to balance exploration and safety. Theoretical analysis demonstrates that the predictive uncertainty decreases as more data is collected, leading to more accurate model predictions. The approach is suitable for real-world applications, particularly in industrial settings where safety is a key requirement.This paper presents a safe active learning approach for time-series modeling using Gaussian processes (GPs). The method addresses the challenge of learning time-series models while ensuring safety constraints are respected. The approach dynamically explores the input space to generate informative input and output trajectories for model learning. The input trajectory is parametrized into consecutive sections, which are determined stepwise based on safety requirements and past observations. A Gaussian process is used to model the time-series function, while another GP is employed to predict safe input regions. The algorithm solves a constraint optimization problem to determine input trajectory sections, taking safety predictions into account. The main contributions of the paper are: (1) Formulating an active learning setting for time-series models with dynamic exploration within the GP framework. (2) Incorporating the safety aspect into the exploration mechanism and deriving an appropriate criterion for dynamic input space exploration. (3) Providing a theoretical analysis of the algorithm and empirically evaluating the proposed approach on a realistic technical use case. The paper evaluates the approach on synthetic data and a real-world high-pressure fluid system. The results show that the method effectively learns time-series models while respecting safety constraints. The algorithm is shown to improve model approximation and safely explore the input space, with the ability to adjust the safety threshold to balance exploration and safety. Theoretical analysis demonstrates that the predictive uncertainty decreases as more data is collected, leading to more accurate model predictions. The approach is suitable for real-world applications, particularly in industrial settings where safety is a key requirement.