This paper reports on the detailed characterisation of the K2-111 planetary system with K2, WASP, and ASAS-SN photometry as well as high-resolution spectroscopic data from HARPS-N and ESPRESSO. The host, K2-111, is confirmed to be a mildly evolved (logg=4.17), iron-poor ([Fe/H]=-0.46), but alpha-enhanced ([{alpha}/Fe]=0.27), chromospherically quiet, very old thick disc G2 star. A global fit, performed by using PyORBIT shows that the transiting planet, K2-111 b, orbits with a period P_b_=5.3518+/-0.0004d, and has a planet radius of 1.82^+0.11^-0.09_R{Earth} and a mass of 5.29^+0.76^-0.77_ M_{Earth}, resulting in a bulk density slightly lower than that of the Earth. The stellar chemical composition and the planet properties are consistent with K2-111 b being a terrestrial planet with an iron core mass fraction lower than the Earth. We announce the existence of a second signal in the radial velocity data that we attribute to a non-transiting planet, K2-111 c, with an orbital period of 15.6785+/-0.0064 days, orbiting in near-3:1 mean-motion resonance with the transiting planet, and a minimum planet mass of 11.3+/-1.1 M{Earth}_. Both planet signals are independently detected in the HARPS-N and ESPRESSO data when fitted separately. There are potentially more planets in this resonant system, but more well-sampled data are required to confirm their presence and physical parameters.