Future perfect tense can be used to look back at an event or occurrence from a time in the future or to make a prediction. The correct perfect tense to be used in this sentence is;
Will have arrived
The future perfect tense can be used to fill up the blank space here. The sentence can thus be rendered thus;
The cruise ship<u>will have arrived</u> at the last port of call before I finished packing.
This indicates that the ship will be at the port before the narrator finished packing. It is like a prediction of something that will happen in the future.
