The relaxation of electron energy by the tail anisotropy instability during lower hybrid current rise in a tokamak is investigated. An unstable tail distribution of electrons is obtained by solving the Fokker-Planck equation combined with a return field and RF associated terms. The quasi-linear relaxation of such an unstable distribution under the influence of plasma waves excited by the instability is examined by evaluating the particle loss due to the toroidal magnetic field ripple. It is found that the energy relaxation on the short timescale of the instability leads to an inward shift of the plasma column, the magnitude of which is of the order of one tenth of the minor radius. The energy loss due to the field ripple on the longer time-scale of parallel diffusion due to lower hybrid waves is also discussed.