Of the month of the Muharram, the first day is considered to be the Islamic New Year. The month is that of grievance and prayers and not celebrations in any way. People have to live under limitations and be attached to Allah Ta’lah from their soul. Prayers for the year ahead and repentance for the year gone past are done in the first month of the New Year.
Even though this is not common, some people have started to exchange gifts and cards on the occasion of New Year.