Does ACE stand for After Common Era?

Yes, some have used (and some may still use) ACE or A.C.E. to identify dates (specifically year numbers) as belonging to the current period of the Gregorian Calendar, which is the calendar commonly used in many countries, especially English-speaking and other traditionally culturally Christian countries, including the US, and is also something of a de facto lingua franca of timekeeping. In this case, it does stand for After the Common Era, and is presumably intended as the converse of BCE or B.C.E., Before the Common Era. The usage seems illogical, however, because the calendar specifies only two periods of time, the Common Era, which is the period we live in, and the period before it, while After the Common Era along with Before the Common Era, suggests three periods of time: Before the Common Era, (In) the Common Era, and After the Common Era, since an era is a period, rather than an instant, of time.

Until the late 20th Century, the most common way to indicate this meaning was with AD or A.D., sometimes thought to mean After Death, but historically abbreviations of the Latin phrase Annō Dominī, which means in the Lord's Year. In more recent years, CE or C.E., for Common Era, has gained widespread acceptance, presumably in an attempt at cultural neutrality.

Note that, except for AD/A.D., all these notations are in English, and that other languages use other notations.