In this work, a Bianchi type-I metric in presence of magnetic field is examined. The model is studied with Tsallis Holographic Dark Energy (THDE) in General Relativity (GR). For obtaining exact solutions which are consistent with recent observations, a power-law relation between metric coefficients and a law of variation for the Hubble parameter H have been considered. The equation of state (EOS) parameter ω_DE>-1 which implies that the model behaves like a quintessence dark energy model. The matter energy density decreases and ultimately tends to zero with the passage of time which indicates that the Universe is expanding whereas THDE density tends to a small value at late times. The magnetic field with due course of time loses its impact. The parameters like matter energy density, THDE density, energy density of magnetic field, Hubble parameter have been investigated graphically. A correspondence between THDE and quintessence scalar field are reformulated to describe the late time acceleration of the Universe. The results obtained were very close to recent observational data.