The weather in North East Greenland can vary dramatically. What you experience will very much depend on the time of year you're visiting Greenland, together with any storms that may hit during your time here. The area Tangent Expeditions is based in generally experiences more stable weather than further down the coast in Kulusuk, making both your time here and your flights in and out more reliable and enjoyable.
Temperatures in the spring may vary from -35°C to +10°C. Most groups would expect to have day time highs of around -20 to -10°C, but this can feel much warmer in sunny, calm conditions. Winter storms can still hit well into the spring, with gale force winds and blowing snow. These are days to spend in your tents! You can expect a few hours of dusk or semi darkness until mid-late April, after which there will be 24-hour daylight.
July and August are a lovely time to be in Greenland, with temperatures rising to over 20°C. Even though the midnight sun will shine well into August, nights can still be well below freezing and a good sleeping bag is a must. On the coast, come prepared for mosquitoes, but these vanish on the mountain glaciers. Storms can still hit through the summer and will often last several days.
Several weather sites are useful to keep an eye on conditions before you fly to Greenland.
Yr.no provides detailed and 2-week forecasts for Constable Point.
Accuweather has a local forecast for the village, Ittoqqortoormiit.
The Met Office surface pressure charts include Greenland, giving a great overview of approaching weather systems.