Luke doesn’t mention the collection Paul made for the poor at Jerusalem, but this is understandable, since Luke’s addressee is Theophilus, Annas’ son and former officiating high priest at Jerusalem, because the Annas family had been mistreating the poor, especially the priests. They had sent men to rob them of their tithes, which some depended upon for life itself. The time is cir. spring of 55 CE, and Paul planed to continue at Ephesus for awhile to preach the Gospel, but he sent Timothy and Erastus to Macedonia (Acts 19:22) to confirm the churches of Europe concerning his intention to bring an offering from them to Jerusalem.
Some scholars conclude that Luke knows nothing of Paul’s collection for the poor at Jerusalem, but it seems that Luke knows something about something, for why is Paul gathering representatives from all over the gentile community to accompany him to Jerusalem (Acts 19:29; 20:4). There doesn’t seem to be a meeting planned, such as in Acts 15, but Luke does have Paul mention a alms and offerings that he had brought for his own nation (Acts 24:17). So, I think there is ample enough in Luke’s Acts to point to the collection for the poor at Jerusalem that Paul mentions in his epistles.
Josephus mentions that cir. 55 CE and afterward that Annas the high priest employed certain villainous zealots to steal the tithes of the ordinary priests at the threshing floors, and some of the poorer priests died of starvation, depending upon those tithes for their living:
8. (180) And now arose a sedition between the high priests and the principal men of the multitude of Jerusalem; each of whom got them a company of the boldest sort of men, and of those that loved innovations, about them, and became leaders to them; and when they struggled together, they did it by casting reproachful words against one another, and by throwing stones also. And there was nobody to reprove them; but these disorders were done after a licentious manner in the city, as if it had no government over it. (181) And such was the impudence and boldness that had seized on the high priests, that they had the hardness to send their servants into the threshing floors, to take away those tithes that were due to the priests, insomuch that it so fell out that the poorer sort of the priests died for want. To this degree did the violence of the seditious prevail over all right and justice. [Josephus: Antiquities of the Jews; 20.8.8; see also 20.9.2 (emphasis mine)].
At this particular time Jonathan, the son of Annas, was reigning as high priest for the second time, replacing Ananias, son of Nebediaus, who had been sent in chains to Rome by Quadratus, governor of Syria, to answer charges of sedition.
The sabbatical year in which the fields would lie dormant in Palestine was coming in the autumn of 55 CE, extending to the autumn of 56 CE. The prior sabbatical year (48-49 CE, see Acts 15) was the year of the predicted famine (cp. Acts 11:28-30; 12:25) when the gentiles previously shared their abundance with the poor at Jerusalem. As stated above, Paul sent Timothy and Erastus to Macedonia (Acts 19:22) in the spring of 55 CE, and Paul intended to spend the winter (55-56 CE) at Corinth (1Corinthians 16:6). He intended to be in Jerusalem by Passover, but a plot on his life delayed him until Pentecost (cp. Acts 20:3), for instead of sailing to the province of Syria (which includes Jerusalem) from Corinth, he returned to Philippi and sailed away from there (Acts 20:6).
 See Josephus: Antiquities of the Jews; 20.6.2