As with his previous novels, Richardson prefaced the novel by claiming to be merely the editor, saying, "How such remarkable collections of private letters fell into the editor's hand he hopes the reader will not think it very necessary to enquire". However, Richardson did not keep his authorship secret and, on the prompting of his friends like Samuel Johnson, dropped this framing device from the second edition.
The novel begins with the character of Harriet Byron leaving the house of her uncle, George Selby, to visit Mr. and Mrs. Reeves, her cousins, in London. She is an orphan who was educated by her grandparents, and, though she lacks parents, she is heir to a fortune of fifteen thousand pounds, which causes many suitors to pursue her. In London, she is pursued by three suitors, Mr. Greville, Mr. Fenwick and Mr. Orme. This courtship is followed by more suitors: Mr. Fowler, Sir Rowland Meredith and Sir Hargrave Pollexfen. The final one, Pollexfen, pursues Byron vigorously, which causes her to criticise him over a lack of morals and decency of character. However, Pollexfen does not end his pursuits of Byron until she explains that she could never receive his visits again.
Pollexfen, unwilling to be without Byron, decides to kidnap her while she attended a masquerade at the Haymarket. She is then imprisoned at Lisson Grove with the support of a widow and two daughters. While he keeps her prisoner, Pollexfen makes it clear to her that she shall be his wife, and that anyone who challenges that will die by his hand. Byron attempts to escape from the house, but this fails. To prevent her from trying to escape again, Pollexfen transports Byron to his home at Windsor. However, he is stopped at Hounslow Heath, where Charles Grandison hears Byron's pleas for help and immediately attacks Pollexfen. After this rescue, Grandison takes Byron to Colnebrook, the home of Grandison's brother-in-law, the "Earl of L."
After Pollexfen recovers from the attack, he sets out to duel Grandison. However, Grandison refuses on the grounds that dueling is harmful to society. After explaining why obedience to God and society are important, Grandison wins Pollexfen over and obtains his apology to Byron for his actions. She accepts his apology, and he follows with a proposal to marriage. She declines because she, as she admits, is in love with Grandison. However, a new suitor, the Earl of D, appears, and it emerges that Grandison promised himself to an Italian woman, Signorina Clementina della Porretta. As Grandison explains, he was in Italy years before and rescued the Barone della Porretta and a relationship developed between himself and Clementina, the baron's only daughter. However, Grandison could not marry her, as she demanded that he, an Anglican Protestant, become a Catholic, and he was unwilling to do so. After he left, she grew ill out of despair, and the Porrettas were willing to accept his religion, if he would return and make Clementina happy once more. Grandison, feeling obligated to do what he can to restore Clementina's happiness, returns to Italy; however, Clementina determines she can never marry a "heretic", and so Grandison returns to England and Harriet who accepts him. They are married; and everyone is accorded their just deserts.
In a "Concluding Note" to Grandison, Richardson writes: "It has been said, in behalf of many modern fictitious pieces, in which authors have given success (and happiness, as it is called) to their heroes of vicious if not profligate characters, that they have exhibited Human Nature as it is. Its corruption may, indeed, be exhibited in the faulty character; but need pictures of this be held out in books? Is not vice crowned with success, triumphant, and rewarded, and perhaps set off with wit and spirit, a dangerous representation?" In particular, Richardson is referring to novels of Fielding, his literary rival. This note was published with the final volume of Grandison in March 1754, a few months before Fielding left for Lisbon. Before Fielding died in Lisbon, he included a response to Richardson in his preface to Journal of a Voyage to Lisbon.

Question: What is Pollexfen's relationship to the protagonist in the story?
Answer: He is one of her suitors.
Alternative answer: He is a suitor to Byron.