Context. The analysis of the composition of primitive C-complex asteroids is essential to understand the distribution of volatiles in the Solar System since its formation. Primitive low-albedo families within the inner main asteroid belt are of particular interest because they are a significant source of carbonaceous near-Earth asteroids, such as Ryugu and Bennu. Aims. This study, part of the JWST SAMBA3 project (Spectral Analysis of Main Belt Asteroids in the 3-μm region), report the first spectroscopic analysis of asteroid (84) Klio in the 3 μm region, in order to better constrain its composition. Methods. We analysed the infrared (0.97-5.10 μm) spectrum of Klio measured by the NIRSpec instrument on board JWST. We used the NEATM thermal model to extract the reflectance spectrum of the asteroid. Several spectral features were then analysed in the 2.8, 3.4, and 3.9 μm regions by different Gaussian fitting. Results. Klio's spectrum shows an absorption band at 2.776 ± 0.001 μm that we attributed to phyllosilicates. We compared the position and shape of the feature with that observed in primitive materials such as carbonaceous chondrites and returned samples from Ryugu and Bennu. The position and shape of the 2.8 μm band, as well as the presence of a 0.7 μm band in the visible, suggest that Klio's spectrum is similar to certain CM2 meteorites. We observed an absorption band around 3.9 μm, with a depth of 0.020 ± 0.001 that could be attributed to carbonates. We could not clearly detect any absorption associated with organics at 3.4 μm.