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We present the characterisation of an inner mini-Neptune in a9.2292005$\pm$0.63 day orbit and an outer mono-transiting sub-Saturnplanet in a 95.50$^{+0.36}_{-0.25}$ day orbit around the moderately active,bright (mv=8.9 mag) K5V star TOI-2134. Based on our analysis of five sectors ofTESS data, we determine the radii of TOI-2134b and c to be 2.69$\pm$0.16R$_{e}$ for the inner planet and 7.27$\pm$0.42 R$_{e}$ for the outer one. Weacquired 111 radial-velocity spectra with HARPS-N and 108 radial-velocityspectra with SOPHIE. After careful periodogram analysis, we derive masses forboth planets via Gaussian Process regression: 9.13$^{+0.78}_{-0.76}$ M$_{e}$for TOI-2134b and 41.86$^{+7.69}_{-7.83}$ M$_{e}$ for TOI-2134c. We analysedthe photometric and radial-velocity data first separately, then jointly. Theinner planet is a mini-Neptune with density consistent with either awater-world or a rocky core planet with a low-mass H/He envelope. The outerplanet has a bulk density similar to Saturn's. The outer planet is derived tohave a significant eccentricity of 0.67$^{+0.05}_{-0.06}$ from a combination ofphotometry and RVs. We compute the irradiation of TOI-2134c as 1.45$\pm$0.10times the bolometric flux received by Earth, positioning it for part of itsorbit in the habitable sone of its system. We recommend further RV observationsto fully constrain the orbit of TOI-2134c. With an expected Rossiter-McLaughlin(RM) effect amplitude of 7.2$\pm$1.3 m/s, we recommend TOI-2134c for follow-upRM analysis to study the spin-orbit architecture of the system. We calculatethe Transmission Spectroscopy Metric, and both planets are suitable forbright-mode NIRCam atmospheric characterisation.

A hot mini-Neptune and a temperate, highly eccentric sub-Saturn around the bright K-dwarf TOI-2134