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Yes, it will work with your existing router. But the issue is, that model is a Wireless N extender. Your Nighthawk is a Wireless AC router. So you won't get the full performance of that router via the extender.
So if you are looking for best performance and faster speed on the extended network, then consider getting the Wireless AC extenders of Netgear. Or any other brand will work. See here --> https://www.amazon.com/NETGEAR-Desktop-Range-Extender-WN2500RP/dp/B00HQ883QW/ref=sr_1_1?ie=UTF8&qid=1501359926&sr=8-1&keywords=WN2500&th=1
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