In Elizabeth George Speare's The Witch of Blackbird Pond, while prayer is certainly mentioned several times throughout the book, there are no official prayer meetings. There are also no moments when after a prayer, Kit sneaks off to meet someone, though she does sneak off many times to meet Hannah Tupper and Prudence. Therefore, in asking about whom Kit met after a prayer meeting, you might be referring to the first time Kit has to join the family for church services at the Meeting House.
In Chapter Five, on the first Sabbath day after Kit arrives at her aunt and uncle Woods's home in Wethersfield, Massachusetts, Kit must attend church at the Meeting House with the family, a service that she hates. She must stand so long her feet ache and the narrow wooden pew bit so much into her legs that sitting was equally uncomfortable. What's more, the townspeople gawk and stare at her in silence, making her feel embarrassed. At the end of the service, "Kit rose thankfully for the final prayer" and left with the rest of the congregation after the minister. Once outside the Meeting House, Kit meets several new people.
The first person she meets is Reverend Gershom Bulkeley. Also, after Kit converses with John Holbrook, whom she met earlier in the story on the ship and who is studying under Reverend Bulkeley, Kit's Aunt Rachel next introduces her to Mistress Ashby and her son William Ashby. The Ashbys are the wealthiest and most politically influential people in the colony. What's more, Kit's cousin Judith plans to marry William, but the moment William sees Kit, he looks at her with an "unmistakably dazzled gaze." Also, when she smiles at him, "William [becomes] speechless."
This proves to be a very important meeting since, after meeting Kit, William stops courting Judith and begins courting Kit instead. He even begins building the house he had no intention of starting to build until he had picked out his bride, meaning Kit. William's interest in Kit drives a further wedge of jealousy between Kit and her cousin Judith until Judith begins setting her cap for John Holbrook instead.