its not as straightforward as that unfortunately.
pardon, i do have the kp3, but never really use the midi side.
But in general, theres no midi message for controlling tempo change. But what can be done is to assign the tempo change function on the synth side to the kp3(using it as a midi controller) and assigning the tap button as the controller to tap tempo.
This is more easier if its softsynth involved and "midi learn/maping" function available.
For hardware, you might have to find out from the synth manual whether is there any continous controller number/message that can be use to control tap tempo within the synth. If there is, then good, you will need to go back to the kp3, use the editor perhaps, to see if its able to assign the tap button to send out this midi message to the hardware. My explanation a rather simplified one, you might need to dwell more into midi info to find out the exact connection to make it work. It wont be clear cut from the start, so do have lotsa patience.
Another way which might be possible to do it, its with synchronizing the midi clock of both devices, kp3 as master and the synth as slave. Basically this one will have to checkout the manual for both equipment in the midi/midi implementaion chart section
Am not too sure the exact details for this, so you might have to check over at the korg forum side for more info.