What you're talking about is a list, although you would need to change the punctuation you used to fit your items into a list (either "horizontal" or vertical). I also had to add some words to your example in order to make it grammatical.
A successful candidate for this position should demonstrate several qualities: sound judgment in complex situations, fairness in the treatment of others, the ability to adapt to other discourses, and so forth.
A successful candidate for this position should demonstrate several qualities:
- sound judgement in complex situations,
- fairness in the treatment of others,
- the ability to adapt to other discourses,
- and so forth.
Here are four resources that discuss the use of colons with lists (although some vertical lists can be styled without colons).
Use a colon before a list when the list is preceded by a complete independent clause. (English Plus)
If the initial clause cannot stand alone and make complete sense, you should not use a colon. (The University of Bristol)
The colon may be used between two independent clauses not joined by a conjunction if the second clause explains, illustrates or enlarges upon the first. (Public Works and Government Services Canada)
The most important thing to remember about colons is that you only use them after statements that are complete sentences. Never use a colon after a sentence fragment. . . . The rules are the same whether you are writing lists or sentences: use a colon when you could use the word namely and after something that could be a complete sentence on its own. (Grammar Girl)
Based on this, and using grammar terminology, an "introductory sentence" preceding a list is just an independent clause. (And the reason I added several qualities to your example was because it was only a sentence fragment without it.)
Outside of this, I've also heard "introductory sentences" called "lead-ins" in plain English.