I am curious as to how Mrs. Clay was introduced to Sir Walter and Elizabeth in the first place; it does not seem very likely that she would be part of their regular social circle so I have taken the liberty to speculate on this subject. Prominent in my speculation is Mr. Shepherd, who is a wily sort of man and I would submit that to be successful with Sir Walter he must be so and I do not disparage him for it. We know that Mr. Shepherd must use a great deal of flattery and often colors the truth with a decidedly “Vanity-friendly” slant to appease Sir Walter’s sense of what is due to him.

“with regard to the gentlemen, there was such an hearty good humour, such an open, trusting liberality on the Admiral's side, as could not but influence Sir Walter, who had besides been flattered into his very best and most polished behaviour by Mr. Shepherd's assurances of his being known, by report, to the Admiral, as a model of good breeding.” (Chapter 5)

We have seen, Mr. Shepherd espouse puffery often for the sake of mollifying the unpleasant business at hand for Sir Walter and Elizabeth’s benefit. Supposing the need for it to be disagreeable or at the very least tiresome, I do not think it at all unlikely that Mr. Shepherd would desire the additional support of a well-looking woman with an acute mind whose flatteries added to his own, could not hinder his success, in fact, with many thanks to Sir Walter’s vanity and incredulity, it might help in persuading him to act rationally. That Mrs. Clay is well qualified and motivated to help her father in this way is verified by Anne when she notes:

“Mrs. Clay had freckles, and a projecting tooth, and a clumsy wrist...but she was young, and certainly altogether well-looking, and possessed, in an acute mind and assiduous pleasing manners, infinitely more dangerous attractions than any merely personal might have been.” (Chapter 5)

Therefore, I have imagined that Mr. Shepherd originally pleaded for his daughter’s introduction at Kellynch Hall by suggesting to Sir Walter and Elizabeth that visiting Kellynch and its inhabitants would be an honor so delightful and unthought-of by Mrs. Clay that her low spirits (unprofitable marriage) and troubled health could not help but be vastly improved, I point to Chapter 5 for potential proof of this “her father had driven her over, nothing being of so much use to Mrs. Clay's health as a drive to Kellynch.” This is again flattery for how is a ride to Kellynch any better for her health than to ride somewhere else? It must be the people inside that make the difference and that Sir Walter and Elizabeth would believe this is no stretch of the imagination as they easily accept it of Mr. Elliot:

“Mr. Elliot had called repeatedly, had dined with them once, evidently delighted by the distinction of being asked, for they gave no dinners in general; delighted, in short, by every proof of cousinly notice, and placing his whole happiness in being on intimate terms in Camden Place.” (Chapter 15)

If her father placed her there as I have suggested he could not have been disappointed with her performance for she easily picks up any foolish or condescending idea of Sir Walter’s and then is able to both support his idea and enhance her father’s argument. In Chapter 3 after Sir Walter says “He would be a very lucky man, Shepherd, that's all I have to remark. A prize indeed would Kellynch Hall be to him; rather the greatest prize of all, let him have taken ever so many before; hey, Shepherd?” Mrs. Clay flatters both Sir Walter’s home and rank and adds to her father’s arguments in support of a Navy man as a tenet by saying “There are few among the gentlemen of the navy, I imagine, who would not be surprised to find themselves in a house of this description. They would look around them, no doubt, and bless their good fortune, but I quite agree with my father in thinking a sailor might be a very desirable tenant.”

Then later in Chapter 3 after Sir Walter’s observations on the naval profession being hard on a gentleman’s appearance “they are all knocked about, and exposed to every climate, and every weather, till they are not fit to be seen. It is a pity they are not knocked on the head at once, before they reach Admiral Baldwin's age.” No one sees fit to discourage Sir Walter from these murderous impulses but Mrs. Clay goes on to gentle the condition of sailors to make Admirable Croft more palatable a tenant and flatters Sir Walter to remember that it is only his kind who do not show their age by saying:

"Have a little mercy on the poor men. We are not all born to be handsome…it is only the lot of those who are not obliged to follow any (profession).to hold the blessings of health and a good appearance to the utmost: I know no other set of men but what lose something of their personableness when they cease to be quite young.

If eventually Mrs. Clay then becomes hopeful of something more than being admitted a fond acquaintance by Sir Walter, I think it is not very hard to see why. Her motivation is great in that she is recently returned to her father’s house by an unprofitable marriage and she has two children whose future is primarily in her hands. That Sir Walter’s weak character makes him easily persuaded and easily fooled may indicate to her that all she really needs is time to make herself indispensable to him and who is to say that with an uninterrupted flow of flattery of his person and never forgeting all that is due to a baronet that she might not be able to do it. I have confidence that she can do it with compliments like this from Chapter 15: "His daughter and Mrs. Clay united in hinting that Colonel Wallis's companion might have as good a figure as Colonel Wallis, and certainly was not sandy-haired.” It is then only to be hoped that if successful, upon Sir Walter’s youth and vigor eventually being cut up at some distant point in time, she might refrain from his advice and nix knocking him out on the head before he becomes disgusting to himself!