The traffic light is red and the green arrow is on. What will the grey vehicle that intends to continue straight ahead do if the yellow vehicle behind it wants to change direction to the right?

Any vehicle that, when the green arrow lights up, is in the lane that other vehicles must use to advance in the direction indicated by the arrow, must advance in that direction (if not possible in its own) even if it was not the direction it wished to take.
In the situation we see in the image, since the yellow vehicle wants to turn, the grey vehicle is also obliged to do so.