Albrecht Giese received his education in Greifswald (Pomerania), Wittenberg and Heidelberg. As was the custom of the time, after his formal studies were over, he toured Europe for several years to learn different languages, as was necessary for a long-distance trader. In the meantime, Giese had married in Danzig. He returned to Danzig from his travels in 1564 and became he became a Ratsherr or councilman. Over the next six years he took part as a delegate of Danzig at several Hanseatic League meetings in Lübeck. His most difficult mission came in 1568-1569, when he accompanied the Gdansk mayor Johann Brandes to a meeting at Petrikau.
After 1560 the king Zygmunt August (Sigismund Augustus) of Poland ordered creation of "Maritime Commission" and royal sponsored fleet with main base in Gdansk. The authorities of Gdansk considered it as a threat for city's interest. Besiedes the members of commission and private owners of war ships (official pirates or kapres) were excluded from city's iurisciction even in criminal cases.
The crisis broke out in 1567. The city council arrested and sentenced to death 11 kapres accused about murder. In response king ordered a commission to revise the constitutions of the cities of Gdansk and Elbing (Elblag). In 1570 the King cancelled their old statutes and declared in force the Statua Karnkowiana, which considerably limited the authority of the city council.
Gdansk had continuously refused to sign any decrees which would take away its written guarantee of autonomy. The Gdansk delegation was treated with greatest misgivings; Brandes was not allowed to speak. These tactics by the crown of Poland were supposed to intimidate the delegation. The four delegates, even after several weeks of degrading treatment and prolonged waiting, were, however, not willing to be forced to sign away the city's autonomy. In 1569 they were brought to Krakow, where they were incarcerated for a year. The intention of the royal government was that this would force the city of Gdansk to agree for the new rules. To make the incarceration more severe, councilman Giese and mayor Kleefeld were jailed at another town than the other mayor and councilman. The Danzig city state council members did not sign and after prolonged negotiations the mayors were allowed to return to their official business after having paid 100,000 Gulden.
Later, in 1576/1577, Danzig was attacked by Stephen Bathory, newly elected king of Poland. After a short war both parts agreed for compromise: Bathory cancelled Statua Karkowiana and Gdansk agreed to pay 200,000 zlotys and confirmed royal suzerenity. Albrecht Giese suffered substantial troubles during this critical time, when he was wrongfully suspected of being friendly towards the Polish king.