I do not think this is supported in the current version of Qt (5.4). You can try using a paint event with QPainter
to draw the text onto the tab in the alignment you want.
You could use specific padding and Qt::AlignLeft
to get this outcome potentially.
See this post on the Qt forum for more info - https://forum.qt.io/topic/35405/qss-qtabbar-text-align-does-not-work