Not running at full power.
The KPS-7 is rated to put out 6 amps continuous, or 7 amps intermittent at 13.8 volts dc.
The TS-440 claims it needs 20 amps to run at 100 watts.
The radio will power up and receive on the KPS-7. It will transmit if you keep the RF power turned way down. Exceeding the current capacity of the KPS-7 by cranking up the RF power too high on the 440 is going to result in it shutting down. Might do it immediately when you key up, or it may take a second depending on how close to that 7 amps you are.
If you want to run the TS-440 at full power, you need a 13.8v power source that will supply the 20 amps that the radio specs call for:
Keep in mind that the current consumption of the radio is based off the manufacturer design, probably with a bit of overhead built in. It probably draws a bit less than 20 amps total, but more than 7 amps. And that 7 amps rating is for intermittent use, like keying up and talking for a little bit, then letting it cool down. The power supply is only rated for 6 amps continuous.