The New Calendar (新暦 Shinreki) is the calendar adopted on Mid-Childa after the end of the Saint King Unification War, replacing the Old Calendar. It has since become a universal time scale in all TSAB-administrated worlds. Apparently, it uses the same month progression and lengths as the Gregorian calendar and it is therefore assumed that one Mid-Childan year corresponds to one Earth year in length. The year numbers in the New Calendar are always padded with zeroes to four digits, similar to the Gundam Universal Century calendar.
An exact relationship between the New Calendar and the Gregorian calendar is never established in the series. However, in the first episode of A's, Hayate's clock shows the date June 3 that falls on Saturday. Years in which such correlation occurs in the Gregorian calender are e.g. 1995, 2000, 2006, and 2017. Since A's aired in 2005, 2006 appears to be the closest match, meaning that Gregorian June 3, 2006 corresponds to New Calendar's June 3, 0065, in other words, the Mid-Childan New Calendar began in the year 1941 (0000) or 1942 (0001) of the Common Era. As noted above, though, this is pure speculation.