Ashton-Kirk is a private investigator.
That is as close to a job description as I could come up with. He would certainly agree with it as would many of those who have come to his door seeking his help in solving perplexing though I am not certain if he actually sought payment for his services.
As is put in the Introduction to him in his first recorded adventure, "Ashton-Kirk, who has solved so many mysteries, is himself something of a problem even to those who know him best. Although young, wealthy, and of high social position, he is nevertheless an indefatigable worker in his chosen field. He smiles when men call him a detective. 'No; only an investigator,' he says. He has never courted notoriety; indeed, his life has been more or less secluded. However, let a man do remarkable work in any line and, as Emerson has observed, 'the world will make a beaten path to his door'.
"Those who have found their way to Ashton-Kirk's door have been of many races and interests. Men of science have often been surprised to find him in touch with the latest discoveries, scholars searching among strange tongues and dialects, and others deep in tattered scrolls, ancient tablets and forgotten books have been his frequent visitors. But among them come many who seek his help in solving problems in crime. 'I'm more curious than some other fellows, that's all,' is the way he accounts for himself. 'If a puzzle is put in front of me I can't rest till I know the answer.' At any rate his natural bent has always been to make plain the mysterious; each well hidden step in the perpetration of a crime has always been for him an exciting lure; and to follow a thread, snarled by circumstances or by another intelligence has been, he admits, his chief delight."
Ashton-Kirk has a fair amount of similarity to another consulting detective, Sherlock Holmes. Both have the well-earned reputation as a solver of mysteries, the more bizarre and arcane the better. Both get involved in cases which puts them in competition with the police, though Ashton-Kirk seems to have a slightly better opinion of the constabulary than the other. Both are true masters of disguise and seem to relish any need to open the stage makeup case and don a new persona.
Being apparently quite wealthy and thus having no need to actually seek regular work or payment for his services, Ashton-Kirk is free to pick and choose his cases. Boredom being something he despises, though, he would likely not turn down any challenge that comes along.
Assisting Ashton-Kirk in his varied investigations is Fuller, described as a "brisk, boyish looking young man". Fuller is not only a good researcher, he is also [my opinion here] in charge of a host of other investigators and fact-checkers that he calls upon regularly to gather the large amount of data on various things which Ashton-Kirk asks for. Exactly how many of these other hands Ashton-Kirk has at the ready in unknown but there seems to be a good number of them, which is good because invariably Ashton-Kirk wants "complete information and I want it quickly".
Ashton-Kirk's membership in this compendium comes about mostly from one recorded adventure but that one does imply on several occasions how Ashton-Kirk has on numerous times acted on behalf of his country handling "several affairs in which the United States government found the investigator's unusual powers of inestimable service. In such matters, tremendous interests often stand dangerously balanced and the most delicate touch is required if they are not to be sent toppling".
As he puts it, "When a crisis arises between two of the giant modern nations, with their vast armies, their swift fleets, their dreadful engines of war, the hands which control their affairs must be steady, secret, and sure. Otherwise an unthinkable horror might be brought about." To assist in such matters, "Experience, steady courage, and sure talent are required in dealing with such things; and these qualities Ashton-Kirk possesses in abundance. To be sure, the departments of the government have the 'Secret Service' at their hand; but the specialist is called in when the general practitioner is at a loss, and he is as much a part of the structure as his regularly employed colleague."
By the way, if you noticed there was no mention of a first name for Ashton-Kirk, it is because I found in none of the pages of his four recorded adventures any reference to one.