Moving from the Ayre AX-7e Integrated amp to the Naim Supernait is, in my opinion, a step down because of its terrific sound quality. I own two Ayre AX-7e amps and like them very much. I have one driving Quad 12L speakers in our family room and another one driving Sonus Faber Auditor M speakers in my living room. My music source is the Ayre CX-7eMP CD Player running balanced cables (XLR) to the amp.
The Ayre AX-7e is a basic two channel integrated amplifier without many bells and whistles. It is a great sounding amplifier. What flexibility does the Supernait have that you are looking for? If you need more control over your system than what the Ayre offers, you may have to change amps (Supernait or what ever else). You should consider what impact another amplifier will have on the sound quality coming through your speakers.
Please note that the Ayre AX-7e Integrated amp sounds much better running with balanced inputs and not RCA inputs. Many reviewers have said this. If your source does not have balanced outputs to your amp, maybe you should look at a source that has balanced outputs (XLR Connections).