We report the first investigation on the effect of applied pressure on the now well-known dimer alpha,omega bis(4,4'-cyanobiphenyl)heptane (CB7CB) that exhibits two types of nematic: the regular uniaxial nematic (N) and the recently discovered twist-bend nematic (N-TB) phase. At atmospheric pressure, the thermal behavior of epsilon(inverted perpendicular) the permittivity normal to the director in the N phase decreases on entering the N-TB wherein the value represents permittivity orthogonal to the helical axis. Application of pressure initially decreases the magnitude of the change in epsilon(inverted perpendicular) and with further increase in pressure exhibits an increase in the value. Such a change in the feature of epsilon(inverted perpendicular) is similar to that obtained at room pressure when the monomeric heptyloxy cyanobiphenyl (7OCB) is doped to CB7CB at a high concentration of 50%. The dielectric anisotropy exhibits a trend reversal with temperature, the extent of which is affected at high pressures. Another salient feature of the study is the effect that pressure has on the Frank bend elastic constant K-33. Over the pressure range studied K-33 enhances by a large factor of 5. In contrast, the splay elastic constant exhibits a much smaller change of only 70%. The pressure temperature phase boundary has a much smaller slope for the N-N-TB transformation than for the isotropic-N transition. We propose that all these features can be understood in terms of the relative population of the more energetic horseshoe and lower energy extended conformer adopted by the CB7CB molecule. The extended conformer is favored at lower temperatures or at higher pressures. This argument is validated by X-ray diffraction experiments at atmospheric pressure on the binary mixture of CB7CB and 7OCB, mentioned above.