The presence of one-dimensional trigonal arrangements of chromium atoms (Cr-3) in the structure of TiCrIr2B2 leads to a magnetic transition near ambient temperature. Herein we report an investigation of the nature of electronic and magnetic properties of TiCrIr2B2 via ab initio calculations together with B-11 NMR Knight shift (K) and spin-lattice relaxation rate (1/T1) analysis. The presence of a characteristic rectangular powder pattern below 280 K, absence of a Korringa relation, strong enhancement of 1/TI.T at low temperatures and weak temperature dependence of K indicate competition between antiferromagnetic and ferromagnetic spin fluctuations in the itinerant d-band electrons, in agreement with ab initio calculations. One-dimensional trigonal arrangements of magnetically active elements in intermetallic compounds, as is found in TiCrIr2B2, are quite rare and could lead to exotic phenomena such as spin-chirality and quantum criticality in low-dimensional frustrated lattices.