This work reports the first theoretical characterization of a manifold of electronic states of the as yet experimentally unknown monotellurium monohydride cation, TeH(+). Both Λ + S and Ω representations were described showing the twelve states correlating with the three lowest (Λ + S) dissociation channels, and the twenty five states associated with the five lowest Ω channels. The X (3)Σ(-) state is split into X1 0(+) and X2 1 separated by 1049 cm(-1); they are followed by the states a 2 (a (1)Δ) and b 0(+) (b (1)Σ(+)) higher in energy by 8554 and 17 383 cm(-1), respectively. These states can accommodate several vibrational energy levels. The potential energy curves of the Ω states arising from the bound A (3)Π, the weakly bound (1)Π, and the repulsive (5)Σ(-) states have a complex structure as shown by the very close avoided crossings just above ∼30 000 cm(-1). In particular, a double minima potential results for the state A1 2 that in principle could be probed experimentally through the A1 2-X2 1 system transitions. The states A2 1, b 0(+), and A4 0(+) offer possible routes to experimental investigations involving the ground state X1 0(+). Higher energy states are very dense and mostly repulsive. The high-level of the electronic structure calculations, by providing a global view of the electronic states and reliable spectroscopic parameters, is expected to further guide and motivate experimental studies on this species. Additional discussions on dipole and transition dipole moments, transition probabilities, radiative lifetimes, and a simulation of the single ionization spectrum complement the characterization of this system.