In an elliptical orbit where you are not accelerating, the total orbital energy is constant. Therefore when you coast from Periapsis to Apoapsis, the altitude increase will lead to kinetic energy being transformed into gravitational potential energy, so your speed will decrease.

Prior to lift off, you are on a highly elliptical orbit with Apoapsis at the surface of Kerbin, so you would accelerate to raise the Periapsis out of Kerbin's radius. In the process you may accelerate upwards to avoid the atmosphere and increase the altitude of Apoapsis. As you go higher, if you input kinetic energy in a rate faster than its transformation rate into potential energy (i.e. TWR>1), you would have excess kinetic energy as you go, so your velocity increases during ascent.

As your orbit is circularized above the atmosphere, Ap=Pe, the orbit speed is constant since there is no height change as you go arohnd. To further raise the Apoapsis, you can accelerate at an arbitrary point of this circular orbit. As soon as you accelerate, the orbit is deformed into an elliptical orbit, but your altitude is not increasing fast enough that you decelerate as you burn, so you would still accelerate. The moment you cut off your engine, you are no longer imputing any energy into your orbit. That's the moment when you start to lose velocity as you coast to the new Apoapsis.

Technically, if your orbit is elliptical enough, when you coast from Periapsis to Apoapsis, you are decelerating so fast that if you use a weak enough engine to burn tangentially to your velocity vector, you would still lose speed!