Accelerating climate change is causing considerable changes in extreme events, leading to immense socioeconomic loss of life and property. In this study, we investigate the characteristics of extreme climate events at a regional scale to -understand these events’ propagation in the near future. We have considered sixteen extreme climate indices defined by the World Meteorological Organization’s Expert Team on Climate Change Detection and Indices from a long-term dataset (1951–2018) of 53 locations in Gomati River Basin, North India. We computed the present and future spatial variation of theses indices using the Sen’s slope estimator and Hurst exponent analysis. The periodicities and non-stationary features were estimated using the continuous wavelet transform. Bivariate copulas were fitted to estimate the joint probabilities and return periods for certain combinations of indices. The study results show different variation in the patterns of the extreme climate indices: D95P, R95TOT, RX5D, and RX showed negative trends for all stations over the basin. The number of dry days (DD) showed positive trends over the basin at 36 stations out of those 17 stations are statistically significant. A sustainable decreasing trend is observed for D95P at all stations, indicating a reduction in precipitation in the future. DD exhibits a sustainable decreasing trend at almost all the stations over the basin barring a few exceptions highlight that the basin is turning drier. The wavelet power spectrum for D95P showed significant power distributed across the 2–16-year bands, and the two-year period was dominant in the global power spectrum around 1970–1990. One interesting finding is that a dominant two-year period in D95P has changed to the four years after 1984 and remains in the past two decades. The joint return period’s resulting values are more significant than values resulting from univariate analysis (R95TOT with 44% and RTWD of 1450 mm). The difference in values highlights that ignoring the mutual dependence can lead to an underestimation of extremes.