I think the responses so far may have missed the core of the OP's question. I think the OP wants to physically REMOVE the brake lever part of the ST-EF500, use the ST-EF500 only as a shifter pod, and install the BL-M315 hydraulic brake lever next to it on the handlebar. Goingbros is this what you're trying to do?

If so, I don't think that's going to work. You'd need to have the EF-500 mounted inboard of the BL-M315, and I think the upper shift trigger, the one you pull to shift into numerically higher gears, will conflict or interfere with the brake lever. You may be able to space the brake lever over just enough for the travel of this trigger to clear it, but then you'd have a pretty long reach over to those shift paddles. I don't think that's going to be a good solution.

Do you have a 3x7 drivetrain or 3x8 drivetrain? Microshift have pretty affordable trigger shifters for either style that will work for you: 7-speed and 8-speed. You could also buy Shimano SL-M310 or SL-M315 shift levers. Both are available in 3x7 and 3x8 to match your bike. Get 'em from a bike shop either local to you or online to ensure genuine Shimano parts. These are very often ripped off by Chinese companies and sold for much cheaper on Amazon or eBay. The fakes may or may not work as well as the real thing.