Mr. Haggerston appears to be a business contact of Edward Gardiner. In his letter to Mr. Bennet announcing that he has found Lydia and Wickham, Mr. Gardiner writes "If, as I conclude will be the case, you send me full powers to act in your name throughout the whole of this business, I will immediately give directions to Haggerston for preparing a proper settlement." Later, in the continued exchange of letters, Mr. Gardiner mentions that "Haggerston has our directions, and all will be completed in a week."
Given the familiar way in which Mr. Gardiner refers to this man, as well as the implication that Mr. Bennet will know who he is, it is likely that Haggerston is a part of Mr. Gardiner's business in some way. As he is occupied in drawing up the marriage contract, it's reasonable to assume that he's an attorney.
