завершать начатое(дословно: подбирать незакреплённые концы корабельных снастей: When one of the employees fell ill, Maria decided to pick up the slack and do his work to ensure that the company didn't come to a standstillvogeler)
перен. принять эстафету(The metaphor comes from the notion of a piece of rope attached to something at one end but lying slack on the ground. So to pick up the slack would be to pull the rope tight. Vic_Ber)