First of all, Fighters are usually faster in base speed and more maneuverable then Runabout or Shuttles. Here is an overview, that you can sort accordingly.
Second, Engine Power equals Speed. Reroute you Power fully to the Engines. You can use the Enhanced Plasma Manifold Console to boost your Speed temporarily. You'll get it by buying the T1 Oberth Science Vessel or by buying the "Console Pack - Enhanced Plasma Manifold / Sabotage Probe Launcher" from the Exchange and chose accordingly. If you can't afford the Console, you can also chose to boost your Speed with Engine Batteries, however the boost is smaller.