new tar paper with to tie in with existing roof tar paper.
Use Ice and water shield in the valley. It can stick to the existing felt, although it would be preferable to cut the existing and slip the I&WS under it. Then install the new felt over the other side of the I&WS.
If you elect to use only felt in the valley, cut a separate piece to lay down the valley and install it under the existing and the new. And then make sure you don't tear it stepping on it.