Is Peter Walsh introduced in Mrs. Dalloway to act as a stimulus to show what Clarissa could have been?
There is of course the sense in which the character of Peter Walsh shows how Clarissa as a character was in the past and compares her to her present stage in life. This occurs at various stages in the text when both Clarissa and Peter remember their past relationship and the kind of familiarity they shared. Consider the following quote that occurs as Peter heads home, passing the ambulance that comes to collect the body of Septimus:
Clarissa had a theory in those days... that since our apparitions, the part of us which appears, are so momentary compared with the other, the unseen part of us, which spreads wide, the unseen might survive, be recovered somehow attached to this person or that, or even haunting certain places after death... perhaps--perhaps.
Peter remembers Clarissa's passion when they were young and in particular how Clarissa found the natural barriers between humans that prevented knowledge and communication so frustrating. She felt that people were like trees in the way that only a small part of them existed above ground to be seen and known by others, and that so much of them exists as a complex and massive root structure beneath ground.
The introduction of Peter as a character therefore does obviously present to us the way that Clarissa has changed over the years, but also at the same time it becomes clear to us that Clarissa is a character who has reached some level of stability and simple contentedness with her life, and that this is a characteristic that Richard profoundly lacks. He not only finds it difficult to know what he thinks and feels but he lives his life as something like a storm as he crashes around, completely unpredictable even to himself. Once they shared a great familiarity, but now, with the passing of years, Richard assumes that Clarissa has become a shallow upper-class woman. If Richard's purpose is to show what Clarissa could have been like, we are thankful that she has settled for the much more stable (if more boring) Richard, and she attains a level of peace that Peter never seems to find.