I am providing some carpet stretching on stairs with before and after pictures. Stretching carpet on stairs need experience and patience. Carpet is stapled on the stairs, so it is not the same way as we stretch carpet on the floor.
In some cases carpet needs to be cut from the riser and put it back on again.
In this open stair example, I had to stretch it to the sideways and staple it back on again. Please take a look at the after pictures.