When you look at the context, the use of "Easter" covers both the Feast of Passover and the Feast of Unleavened Bread.
1Now about that time Herod the king stretched forth his hands to vex certain of the church.2 And he killed James the brother of John with the sword. 3 And because he saw it pleased the Jews, he proceeded further to take Peter also. (Then were the days of unleavened bread.) 4 And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people. (Acts 12)
The translators could have inserted "Pascha" ( πάσχα = pascha) but for English readers they provided the equivalent (which had been a Christian festival for many centuries). Easter has always coincided or overlapped with the feasts of Passover (called Pesach פֶּסַח in Hebrew).and Unleavened Bread.
that's... not entirely accurate.
there has been controversy since pre-Nicene times about when to celebrate the resurrection. many in the church, having been persecuted constantly by the Jews, wanted to distance themselves from the actual feast on which our Lord gave Himself and rose - that being Pesach and the day of firstfruits.
these days are calculated by the lunar calendar, per Leviticus. but some instead calculated by the vernal equinox, and eventually started forcing the day of celebrating His resurrection to land on a sunday - owing most likely to the Christian habit of meeting on the first of the week rather than the 7th, because that resurrection took place on firstfruits, which is always a sunday.
so, eos-tare wasn't a Pesach replacement but a firstfruits replacement.
since eostare isn't marked by the lunar calendar but the equinox, it can be as much as a month apart from Pesach - in fact in the time period of Acts 12 when absolutely no one was celebrating firstfruits by an entirely different calendar, it was probably 30 days different than unleavened bread.
also, since the word ostern doesn't appear in Bible translations until the 1400s, it seems unlikely to be the case that 'centuries' people were celebrating astarte-day by 1500. what they were doing was purposely celebrating firstfruits (part of the paschal week) on totally the wrong day, so that they wouldn't be conflated with Jews by those outside the church.
it seems clear from history that Eos-tar is something added/changed a thousand plus years after Acts 12... so it's not an accurate word in kj translation. it's there because of a human tradition of distancing the church from the actual Jewish feasts that got held over into the text, specifically because the translators were influenced by the whole Luther/Tyndale line of previous work.