In 1987, his family moved to Kamianets-Podilskyi.[1]
Zaremba graduated from Faculty of History (2000) and postgraduate studies (2006) at Kamianets-Podilskyi National Pedagogical University.[1][2] He worked as a representative of the Ukrzovnishintour corporation in Kamianets-Podilskyi (2006–2007) and as a private entrepreneur (provided excursion services), head of the marketing, investment and development department (2011–2016), and since 2016 as the director of the Kamianets-Podilskyi State Historical Museum-Reserve.[1][3][4][5]
He is the founder and head of the Kamianets-Podilskyi Military History Society,[1] which is known for its historical reenactment festivals Terra heroica (2005–2009; since 2010, the Schola millitaria festival),[6] The Last Capital,[6] "Остання столиця"[7][8][9][10] Archaeological Picnic,[2] and Ruthenica Medievalis 2020.[11]
From 2007 to 2011, he was a member of the board of the Ratusha Festival Agency.[2]
In 2017, the Kamianets-Podilskyi Museum-Reserve under the leadership of Oleksandr Zaremba received UAH 7.2 million in revenue.[12]
He runs the YouTube channel Haiduk Kamieniec, where he talks about historical reconstruction, military history of Ukraine, and life in the seventeenth century.[13]