No, won’t work.
Edit: To be more precise: The indexing will be off. The 11 speed road shifters pull more cable for each gear step (each “click”). So you’ll have shifted through the whole 10 speed cassette after 8 or 9 clicks. You won’t be able to shift to certain gears reliably, there will be lots of noise and ghost shifting. Similar to badly adjusted cable tension or a bent derailleur hanger. A 11 speed rear derailleur also won’t solve it since the sprocket spacing is different (they didn’t just add an 11th sprocket).
11 speed road shifters have a different pull ratio than 10 speed (except for the Tiagra 4700 10 speed).
I suggest you try to find a Ultegra 6700 or 105 5700 replacement or change the whole drivetrain to 11 speed.
Edit: When changing to 11 speed in the rear you can probably keep the 10 speed chainrings, front derailleur and left shifter.