Then if you have the harness and all the extra parts, you're all set, except for the motor connector.
I only see 3 pins in the above picture, but are there six more contacts inside?
This is the typical 9 pin"water proof" motor connector, where the end with the pins comes out of the motor.
You would buy the bottom part and splice it to your controller cable. It's not a fun job. I've done it twice, and having lots of experience with exposed electrical connections outside, I worried about the brittle solder joints breaking and mechanical abrasion, etc. It's also not easy to butt solder the 14G wires together. Then there's heat shrink tubing, etc.
If you are going to do this, I recommend buying the above cable, or an extender cable. They're about $15 on ebay. Then remove the old cable from inside the controller. Just cut the wires. Run your new one inside the controller and splice there.
The wire colors should match. I've done about four or five KT controller like this. They always match. It's a lot easier to splice inside the controller. There is plenty of room for a simple twist splice.. No need for strain relief. Protected from the elements. Also, there's no need to take apart the controller as I did in this picture, but it's my clearest photo. It can be done just taking off the top plate, which gives access to all the wires.
If your motor is a geared motor and currently shows speed, and you don't see an external sensor on the wheel, then there is an internal speed sensor already wired into the motor cable. That's typical of most Bafangs. The KT controllers are also automatically wired for that. It will be the white wire inside the 9 pin cable. So when you splice all 9 wires, you're set. You do have to go into the LCD settings and enable the sensor.
If you could find the matching Big 9 connector, you could splice it to your motor cable, but I think you have to leave all the motor hardware (nut, washers, etc) on the cable as they won't go over the bigger connector. Also, now you have a non standard connector. You cannot put your old controller back in, nor will another motor fit. Finally, it's a terrible place for a splice. That's where you want a clean cable that can flex.