The capacity to shift matter from an exotic dimension into ours, and then back out.
Say, for example, you have Universe dimension A, and Universe dimension B. We'll call them USA and USB.
USA and USB both have their own configurations of matter, different from each other. Neither universe interacts in a classical, gravitational sense, however they share a spatial layout. If a star is due galactic center from you in USA, it would also be due galactic center if both the galaxy and the star were shifted into USB. Consider USA to be the air above the surface of the ocean, and USB to be the water and its contents below the surface of the ocean. With the correct application of force from within USA, (a fish hook on the end of a line) you can pull matter and its consequent gravitational pull from USB into USA (You've landed a fish). Once you have made apt use of the matter and its gravitational field, you allow the matter to drop back into its origin dimension (catch and release of the analogous fish)
The matter and its field is utilized in the following way:
A Hegemonic vessel, Baslim, from USA wants to accelerate towards a point elsewhere in its universe. It shifts a sensor into USB, and locates a star inside USB which is between it and its destination. The crew of Baslim shift said star from USB to USA. Baslim then falls towards the star, increasing in velocity as a falling starship is wont to do. Just prior to reaching a particular thermal/Roche threshold, the star is 'released' from USA and shifts back into USB. Baslim then locates another star or gas giant along its trajectory, pulls it into USA, lather, rinse, repeat.
The implications of this method of travel are a theoretically unlimited speed (limited in practical terms by the sensors capacity to detect, shift, and unshift stars as it proceeds) and the capacity for such a shift--drive to function as a weapon. Imagine your planet is a dread enemy of Baslim, and a red supergiant is shifted to within spitting distance of you for a few moments. Other implications include the residents of USB being sorely vexed that their stars are being randomly shifted in and out of their own universe. Such a technology has the capacity to inspire outrage not just across star systems and galaxies, but universes as well.