We propose a new, minimal Majorana neutrino mass matrix texture and study its predictions within a partial tri-bimaximal (TBM) mixing scheme, where \(\sin \theta _{12} = 1/\sqrt{3}\) and \(\sin \theta _{23} = 1/\sqrt{2}\) , with \(\theta _{13}\) and \(\delta \) treated as free parameters. The texture forbids \(\theta _{13} = 0\) and does not correspond to a \(\mu \) – \(\tau \) symmetric structure. As a notable feature, the texture predicts the equality of the Majorana phases. In addition, we find that the predictions show distinct behavior depending on the sign of a single real texture parameter. The texture is realized through a hybrid framework of one Type-I seesaw and two Type-II seesaw mechanisms under an extended symmetry group, \(SU(2)_L \otimes U(1)_Y \otimes A_4 \otimes Z_{10} \otimes Z_{7}\) with properly chosen model parameters. The texture is seen to favor the normal hierarchy for neutrino masses.