When you can see the Northern lights in Svalbard depends on a few factors... The Northern lights, or Aurora Borealis, are basically one huge fantastic light show put on by nature, changing colour depending on the gases in the atmosphere. This phenomenon can be seen in both the Northern and Southern Hemisphere, in the South it is called the Southern Lights, or Aurora Australis. It only happens in these extreme poles because the solar wind particles needed are pulled into place by the magnetic fields (without going into too much technical detail!). The Svalbard Northern Lights aren't considered to be one of the best places for viewing the northern lights owing to a lower concentration of Aurora Borealis in the atmosphere, however they are still very good. The best trip for combining wildlife and northern lights is our Swim with Killer Whales and Humpbacks Safari in Norway in November.
For the best visibility, the night needs to be clear; whether or not there is auroral activity is irrelevant if there are clouds obscuring your view. Summer is not a great time to see them, as it is always light, so any potential activity is masked by the light. Hense, sadly this does not coincide with the best time to see polar bears, due to the midnight sun. During the winter activity by the Auroral Borealis would be clearer as the nights are dark. Although technically they could be there any time of year.