"Acts describes nothing beyond Paul's two-year stay in Rome, even though a number of significant events occurred not long afterwards, including the martyrdoms of James the Less and Mark the Evangelist. Neither does Luke record the outcome of Paul's appeal before the emperor. Thus, we may reasonably conclude that Acts was completed about two years after Paul arrived in Rome, not at any later date. Luke may have spent much of those two years working on his Gospel and on Acts of the Apostles. He may have had some portion of Acts written in advance (notes he had taken along the way and the like). However, this two-year period of time is the most likely time frame for the writing of the bulk of Acts and for its completion."
January 1, 1970
https://en.wikiquote.org/wiki/Acts_of_the_Apostles