The Hayters are the Musgroves’ poor cousins, and Charles, the eldest Hayter son, is the one most likely to make something of himself. His profession is the church, meaning that, in order to get ahead, he’s dependent on 1) influential connections, to line him up for good positions, and 2) current occupants of those positions (like Dr. Shirley) getting old enough to need assistance or pass away. So while he’s on the way up, it’s a slow and boring path that he’s following. This becomes all the more apparent when Captain Wentworth sweeps in and turns the head of Hayter’s potential fiancée, Henrietta Musgrove. And it sure takes the stern application of Louisa’s sisterly concern (and self-interest) to bring Hayter back into Henrietta's favor.
What little we see of Hayter directly, rather than as a pawn in the Louisa-Henrietta-Wentworth triangle, doesn’t leave a good impression. When Anne is being pestered by her toddler nephew, the newspaper-reading Hayter doesn’t bother to get up to help her. While that’s not really enough evidence to make a definite statement of his character, it does suggest that Hayter is not the most considerate of men.