Alfred Hoffy (1790-1860), a Philadelphia printmaker known mostly for his lithographs, is credited with painting the portrait seen here. It is possible the painting was replicated as a lithograph intended for Clay's 1844 campaign, but no such prints are known to exist.
Clay is depicted standing with his dog on the grounds of the Ashland estate. He is wearing his emblematic style of high collar and swallowtail coat.
Read about Clay's style here.
There is a similar painting by John Wood Dodge described here.