A Variable SPEED Drive could technically be anything, such as an AC VFD, a DC drive, even a mechanical vari-drive. Having a display implies it is electronic, but still could be AC or DC. This only matters in terms of WHAT power you are referring to. If you are in North America where the output shaft power would be described in HP, your reference "as in kW" would then imply the electrical power CONSUMED by the complete circuit. Just be aware however that in most places in the rest of the world, kW is also used to describe the output shaft power. That's where the TYPE of VSD becomes relevant.
So assuming you meant CONSUMED electrical power in kW, then you must add the losses in the drive itself, and understand the complexities of how Power Factor is different in an electronic drive system and that the drive losses as a percentage of the total losses increase as speed decreases. That's why, as ScottyUK said, you want to get that more complete picture directly from the VSD if it is available. Most good quality drives have all of the necessary capabilities to do that inherent to their ability to function correctly in the first place, but doing it externally requires attaining that capability to handle those complexities, which means a very expensive meter.
If you have a cheap drive what does not provide true power metering, then the best you can do is an educated guess using assumptions. You will not care about the actual power factor and efficiency at the motor, those are already accounted for in your drive current reading. So you can relatively safely assume that the drive input power factor is .90 and you can assume the drive throughput efficiency is 90%. Both values will probably be better at full speed, but not likely much worse.
"Will work for (the memory of) salami"