You can have your engine speed control set to a particular level but the resulting speed/maneuverability depends on many variables from Driver Coil skill points, inherent ship ratings, and console ratings: impulse engines, warp cores, engineering consoles and possibly console set abilities.
Burst improvements in speed and maneuverability can come from character and BOff abilities.
To increase speed invest more into Driver Coil skill and look to get consoles that have modifiers that enhance the speed/maneuverability.
Tip: It's best to look at consoles that enhance multiple abilities rather than just one, but those are more expensive.
Learn more about these components by searching STOwiki.org.
The engine power level bar in the GUI controls your speed and maneuverability. Generally the faster you go the less maneuverable you can be.
In map and during combat (Red Alert) it controls the impulse speed and maneuverability. Faster the engine goes the less maneuverability.
In map and out of combat, same as above but you can go to Full Impulse.
In sector space (out of a map/warp speed), the power level controls your warp speed. If you are using slipstream, if controls slipstream speed. Warp and Slipstream speeds can be affected by inherent ship multipliers and being granted Diplomatic Immunity and Assign Raiding Party.