Thank you, Gillnetter.
Given "loyalty to the school" is seen as a feature of effective team leaders, I am not sure if your example could work here. On the other hand, I have no idea what the "school" could mean in this context apart from probably some values/ideas/politics shared by a group of people larger than the team - a company maybe. Or could it be synonymous with 'the school of thought'?
Generally speaking, a school is a place where one goes to to become educated. A school has a physical location, or, perhaps a website. A school of thought is a different thing. If you and I agree that XXCVism is a good approach to life, then it can be said that we both belong to the XXCVism school of thought. Effective team leaders can be loyal to the team, they can be loyal to the company, and they can be loyal to each other. I can't see how one can be loyal to a school outside of being loyal to a specific place of education.
I took a look at some of the material from Pearson and noted this - "whether they are students of business English or people already in work".
This incorrect (already in work) statement leads me to believe that the writer is somewhat inept in English. If this is so, then I also can believe that they misunderstand how "school" is used in English. From what you are saying, they somehow have related "school" to mean business, or some other endeavor.
I should probably have said that these characteristics were recommended by Pearson as free resources to accompany 'Market Leader' (see Unit 8). Assuming business language is developing faster than dictionaries, I would really appreciate any help with this sentence.