How can I control a 240v single phase with a separate 240v phase?
Relay is in your question, and Relay is the answer.

(Amazon link because I was there xmas shopping..)

A relay like this has a coil voltage of 220v and is also capable of switching a 220v load.  The coil would be connected to circuit A, and the load/circuit B would be connected to the switched side.

Now, you'll have to select a relay for the size load you have and the type of terminals you want to use, but I believe a relay will do just what you need.

I have a set of relays that control my Christmas lights.  I have the coil side (120v) wired into the light on my porch, and that controls the heavier 20A 120v load circuit that powers the lights.  The light duty programmable light switch for the porch light now controls the 20A of lights.