Study of quantum magnetism in rare earth orthovanadates (RVO4, R = rare earth) is a topic which is currently being investigated by the condensed matter physicists. In this work, through both experimental and theoretical tools, we report the presence of field induced magnetic phase, attributed to fifth order susceptibility, in TbVO4, at low temperatures. The structural transition reported around 31 K, results in the formation of pseudospin—$${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}$$
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doublet ground state separated by an energy δ. Temperature dependent heat capacity indicates toward an increment in δ, on application of magnetic fields. Above 10 kOe, the Zeeman energy associated with magnetic anisotropy strengthens, resulting in an enhanced splitting of the pseudo-doublet ground state. This increased splitting stabilizes the magnetic phase associated with higher order moments. These observations are further supported by our theoretical model to evaluate δ, as a function of applied field. Our study provides a platform to study the possible presence of higher order moments in other Jahn–Teller systems.