Why is it "the UEFA board" not "the UEFA's board"?

Solution 1:

If UEFA is pronounced (or possibly even only thought of) as an initialism, standing for Union of European Football Associations, then the definite article is required. In this case, the article relates to the noun immediately following, that is, UEFA not committee:

A member of the Union of European Football Associations' executive committee...
A member of the U.E.F.A.'s executive committee...

A member of the UN's Security Council...
An example of an NGO's operations is...

If UEFA is pronounced as a single word /ju:ˈeɪfə/, it's treated as a name. Names don't get the definite article.

A member of UEFA's executive committee...

A member of London's police force...

If it's not a possessive, then UEFA becomes an attributive noun, which functions as an adjective. The article is then governed by the head noun, committee.

A member of the UEFA executive committee...
A member of a UEFA committee...

A member of the UN Security Council...
An example of NGO operations is...