What is the proper usage of a verb when the subject is singular but its meaning is plural?

Phrases of the form "a(n) [singular noun denoting a group] of [plural noun]" are sometimes treated as singular, and sometimes as plural. One major factor is the first noun; to take an extreme example, I believe that all forms of English allow "a lot of people agree" and forbid *"a lot of people agrees". Another major factor is the language variety; UK speakers are typically much more willing than US speakers to use a plural verb with a syntactically-singular subject.

In your specific example, I think the deciding question would be — is it the actual set of icons that suggests the change? Or is it the icons in that set? If the latter, then "a new set of icons" will generally be treated as plural.