Can my current router/modem be used as a router for my new modem?

[tallsheet673]

I have been using my current "all in one" router/modem (there's probably a term for I just don't know it) to stream internet for about 2 years now. Well I've been having trouble with my speed so I called my internet provider and they upped my speed at no cost and sent me a modem that could stream it, in case what I had wasn't sufficient. Well I got it in, expecting to see what I already had, but it was just the modem. It's saying on the instructions that I need a router to attach it to. Now I'm not the most tech savvy so all this could make me look pretty stupid so here's my question: can I use what I currently have as a router and just hook up the modem that they sent me? I should end by saying I did a speed test without doing anything and the numbers that I got match what I should be getting on my plan. Is it worth hooking up what they sent me or should I just leave in what I have? And if it's best to hook up the new one what is the best way to do it with the equipment that I currently have? Preferably without buying anything else