You can unlock new vehicles by progressing through Championship Mode.

Vehicle	How to unlock
Fulcon Capital	Beat the Xenon Cup in Subsonic League.
Mueller PLS	Beat the Cobalt Cup in Supersonic League.
Rochdale Trust	Beat the Titanium Cup in Supersonic League.
Spaarc Unlimited	Beat the Cobalt Cup in Subsonic League.
Willard Labs	Beat the Xenon Cup in Supersonic League.
XIsle GMBH	Beat the Titanium Cup in Subsonic League.
Zvil Corporation	Beat the Cobalt Cup in Hypersonic League.