We performed second harmonic generation (SHG) measurements in the nematic liquid crystal formed from polar aromatic polyester which comprises 4-hydroxybenzoic acid and 6-hydroxy-2-naphthoic acid in a molar ratio of 73/27. The polymer is commercially available and called Vectra. The shear-oriented nematic liquid crystal of Vectra shows strong SHG mostly along the n-director. Since no electric poling is made, the observed SHG activity indicates that the polar ordering is spontaneously formed in the nematic liquid crystal. From detailed analyses of the SHG intensity profiles measured with combinations of polarizer and analyzer directions to the n-director, the nematic liquid crystal is found to possess the C-s packing symmetry; in other words, it is not uniaxial but biaxial, and the polarization arises in the symmetry plane. To search the origin of the spontaneous polarization, we prepared a series of Vectra polymer with various degrees of polymerization (DP) and two chemically modified Vectras. Of interest is that the DP of polymer significantly affects the polar structure. When DP is decreased, the SHG activity in the nematic liquid crystal disappears completely. Since the dipole moment increases with DP, the huge dipole moment of polymer is considered to be responsible for the polar ordering. In one of the two chemically modified Vectras, terephthalic acid (TA) and biphenol (BP) in an equimolar content are introduced. As expected from the dissipation of head-tail character in constituent polymer, the nematic liquid crystals lose completely the SHG activity only with an incorporation of 5 mol % of TA and BP. In another modified Vectra including 3-hydroxybenzoic acid (m-HBA), the head-tail character is not lost, but their liquid crystallinity is destabilized because of kink conformation induced by the m-HBA unit. In this system, the SHG is invariably observed for the nematic liquid crystals, but as one of the significant effects, polar biaxial nematic liquid crystal of Vectra is altered to the polar uniaxial one by the introduction of m-HBA above 5 mol %.