Singular or plural following a list

Solution 1:

You should use "inspire".

Don't be distracted by the fact that there's only one leader. The inspiration is being done by that leader's many fine qualities, which are obviously plural.

I assume you wouldn't have doubts about Two great leaders whose vision inspires all (if you do, try it again as Two great leaders whose shared vision inspires all).

Solution 2:

There is a lot going on in this sentence but part of the problem is that it is a sentence fragment.

An extraordinary leader whose vision, values, integrity and boundless curiosity inspires all who follow in his footsteps.

If we trim out the list:

An extraordinary leader whose [list] inspires all who follow in his footsteps.

Then trim the extra clause and adjective:

A leader whose [list] inspires all.

This isn't a sentence. You need something else:

I am a leader whose [list] inspires all.

A leader whose [list] inspires all has arrived.

Once you have this in place you can ask about the inspiration. Since the inspiration is stemming from the list and not the leader you should follow the plurality of the [list]. If we stick a single word in there we can see why:

A leader whose horses inspire all has arrived.

A leader whose horse inspires all has arrived.

So, to actually answer your question, when using a list, always treat it as plural. See also: “My apples and orange are wrong”, specifically the accepted answer.