Would you capitalize the job title in the following sentence?
I am writing this letter in regard to Joe Brown who is applying for the director of teaching and learning position in the XYZ School District.
The Chicago Manual of Style says not to capitalize a title when it appears alone like that. Nor should you cap it when it appears in apposition, such as (if your candidate gets the job),
Joe Brown, director of teaching and learning
You cap formal titles when they appear before someone's name,
Director Joe Brown
though not every title is meant to be used in that way... for instance, if you were talking about Steven Spielberg, in most contexts you would say
director Steven Spielberg
because in most contexts you wouldn't be ascribing a formal title to him, but merely describing what he does.
The rule is that when a title immediately precedes the name, e.g. "Director Joe Brown," then the job title is capitalized, but not when it comes afterwards. See, e.g., GPO Style Manual § 3.34. Exceptions are made for especially important positions like President of the United States or Queen of England. Ibid. § 3.35. The GPO Style Manual gives the example: "Charles F. Hughes, rear admiral, U.S. Navy: the rear admiral." In your sentence, Mr. Brown doesn't even have the job, so director would be lower case.