expected from a person 點解 ?

句子其實有個 that/what 字、不過巳被省略。

A director need not exhibit a greater degree of skill than that may be expected from a person of his knowledge and experience.

A director need not exhibit a greater degree of skill than what may be expected from a person of his knowledge and experience.

而 that 在句中是指 skill。what 是指某東西，在句中也是指 the degree of skill。

中文意思是
董事不須要展示出較他知識和經驗為高的能力。

要求董事的能力只需同他有的知識和經驗相稱。

可以寫成兩句嗎﹖
that/what may be expected from a person of his knowledge and experience.
是一個名詞性分句(noun clause)，全句應是一句為佳，這句類似法律條文固此會較複雜，日常用語可作以下寫法

A director need not exhibit a greater degree of skill than his knowledge and experience allow.

'Need' is not commonly used as an auxiliary verb nowadays, but formerly it was.
A director need not...= A director does not need to...
(Ref: http://en.wikipedia.org/wiki/English_modal_auxiliary_verb#Dare_and_need)

全句大約是
董事不一定要展示出較一般人為高的知識和經驗.

英文可改寫成
A director's knowlege and experience needed not exhibit a greater degree of proficiency than any other person.