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Adaptive responses are probably the most effective long‐term responses of populations to climate change, but they require sufficient evolutionary potential upon which selection can act. This requires high genetic variance for the traits under selection and low antagonizing genetic covariances between the different traits. Evolutionary potential estimates are still scarce for long‐lived, clonal plants, although these species are predicted to dominate the landscape with climate change. We studied the evolutionary potential of a perennial grass, Festuca rubra, in western Norway, in two controlled environments corresponding to extreme environments in natural populations: cold–dry and warm–wet, the latter being consistent with the climatic predictions for the country. We estimated genetic variances, covariances, selection gradients and response to selection for a wide range of growth, resource acquisition and physiological traits, and compared their estimates between the environments. We showed that the evolutionary potential of F. rubra is high in both environments, and genetic covariances define one main direction along which selection can act with relatively few constraints to selection. The observed response to selection at present is not sufficient to produce genotypes adapted to the predicted climate change under a simple, space for time substitution model. However, the current populations contain genotypes which are pre‐adapted to the new climate, especially for growth and resource acquisition traits. Overall, these results suggest that the present populations of the long‐lived clonal plant may have sufficient evolutionary potential to withstand long‐term climate changes through adaptive responses. [ABSTRACT FROM AUTHOR]