This is the 10632nd most frequent Russian word.
возглавляемой
"Led by" or "headed by."
The word "возглавляемая" here is used as an adjectival participle describing the program as being led by the school principal, indicating action and agency.
Программа, возглавляемая директором школы, принесла учебному процессу новые идеи.
The program led by the school principal brought new ideas to the educational process.
In this sentence, "возглавляемая" describes the company, emphasizing the leadership role of the entrepreneur in its quick success.
Компания, возглавляемая известным предпринимателем, быстро вышла в лидеры рынка.
The company led by a famous entrepreneur quickly became a market leader.
Here, "возглавляемый" is modifying the noun "проект," illustrating that the group of scientists is overseeing or directing the project.