The exterior finish plays a roll into it. Brick, stone, or ?. Is there interior work like soffit, beams, etc? Size of windows and if they're side by side with support in between. Too little information was given for any type of answer.

Are you in a historic district? Fenestration changes may be prohibited or need approval.

Is the whole window low, or does it go down lower than you want? It would be simplest just to replace the big window with a smaller one. We did that in both our kitchen and bathroom. That way you keep the existing header, and just frame out new support for it from below. And fill in the exterior, whatever it is. Ours is vinyl siding, so it was easy peasy.

Thank you so much weedyacres - thats exactly it. The window goes lower than we want. Very helpful - thanks!

We wanted to move a kitchen window up a few inches because it came down to the counter, and water collected there, causing a mold problem. I naively thought it could just be raised a few inches, and we'd only have to worry about repairing the exterior. Wrong. A header above the window could not be moved (or not without considerable changes), and we ended up having to install a new window. So, as others have noted, what's involved all depends.