Not easily.
You can't forward the signal from your smart TV to the other one. So you'd need:
(a) a Netflix account that lets you stream to two devices (which, according to this, costs three quid a month extra:
http://www.express.co.uk/life-style/science-technology/583690/Netflix-UK-Subscription-Standard-Price-Plan-Increase ) ; and
(b) a way of streaming that second signal to your non-smart TV, such as buying a Chromecast (which plugs into a USB socket on your non-smart TV, if you've got one), receiving the Netflix stream on your PC, laptop, tablet or phone and then streaming across it to the Chromecast.