All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
We do not find a religious impediment to sending such cards for commercial purposes and encouraging clients to make future deals with the company in the new year. What matters is that these cards do not include congratulations for the new year or Christmas. There is no harm in using the Gregorian calendar as far as the worldly affairs and dealings are concerned, like for appointments, travels, commercial deals, and the like. The scholarly view adopted at Islamweb in this regard is that it is more appropriate to use the Hijri calendar in worldly affairs needed by people because this would constitute purposefully acting differently from the disbelievers. However, there is no harm in using the Gregorian calendar for worldly affairs in case of need.
This is contrary to the case with religious obligations that are related to the lunar months such as fasting, zakah, Hajj, ʻiddah (waiting period) for Muslim women, and the like. The Hijri calendar must be used for these obligations.
For more benefit, please refer to fatwa 91201.
Allaah knows best.