AC Supply has three wires: Black, White and Red to Ceiling Fan.
Want to connect Harbor Breeze Remote Control, which has White and Black AC.
Connecting Black to Black, white to white, and blue to blue to the fan. Where do we connect the Red AC line to?

Well we really need to know some more information. For example, is the AC source in the ceiling or is being brought to a wall switch?

Does your fan have a light package?

Normally, the black feeder goes to the black for the fan.

White goes to white.

And red would go to blue for the light.