In line 13, "Art is long" is used in contrast to the "fleeting" nature of time. This line means the constructions of a man's record of experience [art] may last long after him as a witness to his talent and creative imagination, but the time a person has to create art is limited.
Certainly, art (this includes paintings, sculpture, music, and literature) is a form of communication of the human experience, all of which often lasts for ages. Nevertheless, the artist possesses only a "fleeting" amount of time in which to form his/ her work of art. Therefore, the artist must find it necessary to work diligently and with perseverance within the limitations of a lifetime. This fact is another part of the speaker's argument that one must "Act,—act in the living Present!" (line 23).
There is little doubt that Longfellow's "A Psalm of Life" stresses what is thematic of carpe diem verses, yet it also includes more, as in the idea that what one does in life can remain long after he or she is gone. Unlike traditional carpe diem poems, Longfellow's verse includes the theme of making the most of one's life in order to fulfill oneself, but also in order to leave something of worth behind for others. By doing so, others may find its beauty, value, and lessons to be learned in "the footsteps of time" and "take heart."