At the conclusion of the Jerusalem Council, James told Paul not to forget the "poor." At the time, Paul seemed quite eager to help in this regard. According to Paul's letters, he gathered a collection of money from all the Gentile churches to be used for the "poor" in Jerusalem. He talks about it often and perhaps even risked his life to present it, yet Luke never mentions it in Acts after Paul arrived. Why not?
It is well known that the members of the early church in Jerusalem shared everything in common. This was done in part because people believed that time would be short before Jesus came again. It was also done to promote equality and care for the poorer members. But as time went on, resources in Jerusalem dwindled and the church was struggling financially. Paul did seem eager to help raise money for them.
Paul is on record in his letters to several churches encouraging them to take a collection each week (1 Cor. 16:1-2). He makes the point that this is the same request he had made of the Galatians. Later, in 2 Cor. 8:3-5, he claims that the churches from Macedonia had far exceeded his expectations in the amount they had raised for the poor. In Romans 15:25ff, he stated he was going to Rome to deliver the money, and that the Gentile churches had contributed material blessings freely out of gratitude for sharing in the spiritual blessings. He obviously spent a lot of time working on this effort. At one point, it seemed that some believers questioned whether or not he was skimming off the top. His response in 2 Cor 12:14-18 refuted this notion wholeheartedly.
While there is no doubt that his motives were pure, Paul also hoped to use this collection as a goodwill gesture from the Gentile churches. The Jerusalem Church was mainly comprised of Jewish Christians, and this was his way of trying to reconcile the two groups. He might also have thought that, if the elders in Jerusalem saw his efforts, they might be more amenable to the work he had been doing with the Gentile churches.
When he was on his final leg of his third missionary journey and about to depart for Jerusalem, he uncovered a plot against his life. That necessitated an immediate change of plans, and he decided to go back by land through Macedonia. Luke includes mention of a whole list of people who accompanied him from the various churches that he visited. Some scholars think the cities sent them as delegates to accompany Paul in delivering their contribution to Jerusalem.
From his letters, we know that Paul was adamant about taking this collection back to Jerusalem. And some scholars think it might have been the reason he insisted on going there, even though it was fraught with danger.
So, why doesn't Luke mention anything about the collection when he arrived in Jerusalem? Maybe one of the biggest reasons is that scholars think things didn't go all that well. Maybe they didn't even accept the money. According to Paul's letters, this journey to Jerusalem is for the express purpose of delivering the collection. In Luke, however, the journey is presented as part of the divine plan. Paul has been divinely impelled to go there. And he was obedient.
Yet, Luke does give some hints that Paul has money at his disposal. He is not long in the city before he is asked to underwrite the sacrifices required for a purification ceremony. Four men had taken a special Nazarite vow, which would have lasted for 30 days. During that time, they would fast, pray, and essentially withdraw from society. At the end of that period, there would have been a great celebration that included multiple sacrifices. Paul agreed to sponsor them as well as to participate in the Levitical rite of purification for himself.
Ironically, it was this move towards purification that landed Paul in prison when he was accused of violating the sanctity of the temple by inviting a Gentile into holy space. (The charges were untrue, but the authorities put him in prison to save him from the motley mob.)
Another hint of money comes in Paul's encounter with Felix and his wife. They visited often with Paul and talked with him. It says that his wife, Drusilla, was a Jewess. No doubt they had great conversations, but it is doubtful whether Felix took them to heart, because it says, "he was hoping that Paul would offer him a bribe, so he sent for him frequently" (Acts 24:26). Soliciting or accepting a bribe would have been patently illegal, but it was known to happen. Plus, while no bribe was ever offered, it suggests that people knew that Paul might have had access to a lot of money – such as the collection money.