A double layer (DL) is created in a plasma when the plasma is perturbed in the presence of a temperature anisotropy. We derive a new simple theory for the existence of an unstable, non-oscillatory electrostatic DL-like structure in the presence of a magnetic field gradient in a collisionless plasma with a temperature anisotropy in the direction perpendicular to the magnetic field. The DL is treated as a wave perturbation in the plasma using kinetic theory with a gyro-kinetic approximation to obtain a dispersion relation. The presence of an electron temperature anisotropy is the necessary condition to obtain an exponentially growing instability, and the corresponding growth rate is found to be the ratio of the electron kinetic energy and the electric field energy across the DL region. The theoretical predictions are then validated against a one-dimensional electrostatic particle simulation carried out in a traveling magnetic field thruster environment. An anisotropy ratio parameter was introduced, and the theoretical growth rates were found to be in good agreement with the simulation for different anisotropy ratios. An ion beam, associated with the DL dynamics, is observed within the simulation domain. A parametric study revealed that the DL-like structure loses its ambipolar shape for temperature ratios less than 10. It has been found that a stronger anisotropy is required to obtain the DL-like structure.