In united states federal income tax law, a qualified subchapter s trust is one of several types of trusts that may retain ownership as the shareholder of an s corporation. Jan 4, 2025a qualified subchapter s trust (qsst) is a specific type of trust that allows individuals to hold shares in a subchapter s corporation while complying with the requirements set by the internal. Grantors/shareholders can use the qsst to make a gift of all or part.