Sales company Beta Cinema has picked up the eco-thriller “The Climb,” starring Cara Delevingne. Based on true events, the film tells the story of a Greenpeace-led protest action against Shell’s plans to drill in the Arctic, when female activists scale the tallest building in Europe, London’s Shard.

Delevingne will play one of the leads as the daredevilish-climber who is the head and heart of the venture. Since her 2012 acting debut in Joe Wright’s “Anna Karenina,” Delevingne has starred in “Paper Towns,” the film adaptation of the John Green novel, DC Comics’ “Suicide Squad,” Luc Besson’s space opera blockbuster “Valerian and the City of a Thousand Planets,” Michael Winterbottom’s “The Face of an Angel,” Alex Ross Perry’s “Her Smell,” and “Life in a Year,” opposite Jaden Smith.

The film is the directional debut of leading visual effects art director Hayley Easton Street, whose credits include “Justice League,...