Yes, you can do it. Though someone tell that change the frames only may cause vision blur because the PD of the lenses may not right for your eyes, i still replaced my ugly old eyeglasses frames. Now, my eyeglasses have worn for two years. And it works good for my eyes and there is not such phenomenon like vision blur. I still get clear vision from the eyeglasses. So, good luck.
You probably can put your old lenses into new glasses frame. But make sure the new frame can fit your old lenses properly. When you choose the new glasses frames, you should take the centering of the lenses into account. The centering of the lenses must be exact to your iris, or it will not provide you with clear vision because you always look through the centering of the lens. So it is a hard job to put old lenses into new glasses frames. The best way is to get a new pair of glasses.