The new Power he was referring to was actually Sauron. If you read the books that bit of dialogue is actually taken from Gandalf's account of his encounter with Saruman at Isengard where Saruman betrayed and imprisoned Gandalf.
The full quote from the book:
"And listen, Gandalf, my old friend and helper! " he said, coming near and speaking now in a softer voice. "I said we, for we it may be, if you will join with me. A new Power is rising. Against it the old allies and policies will not avail us at all. There is no hope left in Elves or dying Númenor. This then is one choice before you. before us. We may join with that Power. It would be wise, Gandalf. There is hope that way. Its victory is at hand; and there will be rich reward for those that aided it. As the Power grows, its proved friends will also grow; and the Wise, such as you and I, may with patience come at last to direct its courses, to control it. We can bide our time, we can keep our thoughts in our hearts, deploring maybe evils done by the way, but approving the high and ultimate purpose: Knowledge, Rule, Order; all the things that we have so far striven in vain to accomplish, hindered rather than helped by our weak or idle friends. There need not be, there would not be, any real change in our designs, only in our means."
Tolkien referred to the angelic beings, the Ainur, who participated in the creation of Arda by song as "Powers" throughout the Silmarillion and LOTR, IIRC.
