You may be able to get it to work by adjusting the cable tension on the rear shifter. Turn the adjuster in (clockwise as you look down at it) 1/4 turn, and see if that resolves it. If not try another 1/4 turn. Repeat until it gets better, or worse. Keep track of the number of 1/4 turns, so you can go back if reducing the tension doesn't fix it.

Was the old chain badly worn? If so, and the cassette is now worn, you will have skipping issues anyway.