Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting. \cite{bui2017streaming} developed an efficient variational approach to train online GPs by using sparsity techniques: The whole set of observations is approximated by a smaller set of inducing points (\textbf{IPs}) and moved around with new data. Both the number and the locations of the IPs will affect greatly the performance of the algorithm. In addition to optimizing their locations, we propose to adaptively add new points, based on the properties of the GP and the structure of the data.