It depends very much on the new use. If you find out that ASS (the stuff in Aspirin)
helps against ingrown toenails (oh, no, wait, somebody already found that) cures hearing loss induced by trauma, you can patent the use of ASS against hearing loss by trauma.
And to extend the previous answer, if the patent for ASS only patents the use of ASS against headaches, you will not even need their patent. If however they protected the method of producing it, you may not produce it without a license.
If however you found out that you can use a LAN compression protocol for WLAN, this might be considered obvious, in this case you would not get a patent. It might even be infringing the old patent for the protocol if this patent was well written and stating the use of the protocol in any kind of data transmission for example.
I realize I might have misunderstood the question. If it was about combining known products into a new product, the answer is yes, that's patentable. Most inventions are a combination of known known things. Think a car. Wheels were known, motors were known, etc. But the combination of them made a whole new thing.
It is therefore possible to be inventive by combining old products. For this to be enough for a patent, the combination as such has to be novel and the prior art (the components, maybe a different combination of similar components) should not hint their use in such a way.
However to produce/sell/use this new invention, you might need to license the patents for the components. For this, check if your invention is still literally doing what the patent claims (and more, but it if part of your invention infringes the patent, producing it will infringe the patent).