Age
The narrator says that he appears to be “five or six and twenty.”
Family and Situation
Mr. Palmer is the husband of Mrs. Charlotte Palmer née Jennings. They seem to have married within the past year (as Charlotte participated in last Season as an unmarried woman) and Charlotte has their first child in February, suggesting the wedding occurred last May at the latest.
We also know that Mr. Palmer has a “near relation...who lived a few miles on the other side of Bath” from Cleveland. Charlotte removes from the house, with the baby, to this relation’s house when Marianne falls ill.
Mr. Palmer lives at a stately home called Cleveland in Somersetshire with his wife. As of the late autumn, he is running around the countryside canvassing for an upcoming election for Parliament. Charlotte speaks as though he is sure to win, but the likelihood of this is less clear; she does mention that Mr. Palmer won’t call on Willoughby because “he is in the opposition."
Mr. Palmer also appears to have a house in Hanover Square, which is unsurprising, given his political aspirations. When the baby announcement goes through the newspaper, he is referred to as “Mr. Thomas Palmer, Esq.” which likely reflects his own social aspirations and/or machinations to get into Parliament -- he almost certainly would have put the announcement in himself.
Connections
The Palmers appear to be acquainted with a family called Weston who comes to stay with them in the autumn, shortly after Edward Ferrars’ visit to Barton Cottage.
Appearance
We are told he “was a grave looking young man...with an air of more fashion and sense than his wife, but of less willingness to please or be pleased.” Upon first meeting the Dashwoods, “He entered the room with a look of self-consequence, slightly bowed to the ladies, without speaking a word, and, after briefly surveying them and their apartments, took up a newspaper from the table, and continued to read it as long as he staid.”
Character
In many ways, Mr. Palmer shows the reader what Edward Ferrars might be if he chose -- including political aspirations, a wife with a wealthy dowry and a lackadaisical lifestyle.
With some affection, Charlotte calls Mr. Palmer “quite rude” and insists that he contradicts everybody. In particular, she identifies the impending election as the source of some exhaustion, insisting “it is very fatiguing to him! for he is forced to make every body like him.” We also hear through Mrs.Jennings that Mr. Palmer professes indifference to his own baby, stating that nothing is exceptional about it. We also know he can be quite restless; on a day rainy day at Barton, he exclaims "Such weather makes every thing and every body disgusting. Dullness is as much produced within doors as without, by rain. It makes one detest all one's acquaintance. What the devil does Sir John mean by not having a billiard room in his house? How few people know what comfort is! Sir John is as stupid as the weather."
Elinor observes this behavior as not stemming from true cruelty of heart but “It was rather a wish of distinction...It was the desire of appearing superior to other people. The motive was too common to be wondered at; but the means, however they might succeed by establishing his superiority in ill-breeding, were not likely to attach any one to him except his wife.” Later on, Elinor perceives this tendency to come from an idea that he is as superior in understanding to everyone as he is to his wife and her mother.
In spite of the prickly exterior, it would seem Mr. Palmer does bear genuine affection for his family. Charlotte tells a story about him concealing his plans to travel to Barton--where her family is--“till the carriage was coming to the door” and then asking her if she would be willing to set off with him. When Elinor stays at Cleveland, she is surprised to find him “very capable of being a pleasant companion” and even decides that he is “fond of his child, though affecting to slight it.” When Marianne later falls ill, Mr. Palmer is reluctant to leave the Dashwoods alone in the house “from real humanity and good-nature, as from a dislike of appearing to be frightened away by his wife,” until he “was persuaded at last by Colonel Brandon to perform his promise of following her.”
Hearkening somewhat to Mr. Bennet, Elinor observes “His temper might perhaps be a little soured by finding, like many others of his sex, that through some unaccountable bias in favour of beauty, he was the husband of a very silly woman,—but she knew that this kind of blunder was too common for any sensible man to be lastingly hurt by it.”
Habits and Hobbies
Once she gets to know him, Elinor assess Mr. Palmer to be much like many of the young gentleman of his class: “He was nice in his eating, uncertain in his hours; fond of his child, though affecting to slight it; and idled away the mornings at billiards, which ought to have been devoted to business.”