Businesses will raise their voices, making common cause with pro-European MPs, the Treasury (in the person of Philip Hammond, the chancellor of the exchequer) and a newly thrusting, liberal wing of the Tory party (led by George Osborne, his predecessor).
http://dictionary.cambridge.org/dictionary/english/thrust
As you can see it has meaning of "to push suddenly and strongly" Does it mean the liberal wings are violent or they are growing suddenly?
I think that this is probably a reference to how the rocket launch process is initiated in the space industry. The rocket thrusts the burning gases downward to make it move upwards. So, newly thrusting probably means that this new political project has been recently launched and it's currently in the process of gaining momentum just like a rocket does when it blasts off of the ground.
We can also add to this what Tᴚoɯɐuo's description from the comments section that the author wants us to understand newly thrusting as a synonym for recently exerting considerable influence.
