The quoted title of this poem from Clark Ashton Smith (CAS) references the sixth stanza of John Milton's "Lycidas":
Fame is the spur that the clear spirit doth raise
(That last infirmity of noble mind)
To scorn delights and live laborious days;
Milton's poem eulogized Edward King, a friend who died by drowning. "Lycidas" suggests that King will achieve fame, but necessarily after his death.
CAS' short poem has a different take:
Fame is the passing of a fitful wind—
A shouting of the tempest, and the sigh
That lingers in the sunset-ending sky,
To stillness and the alien stars resigned.
These lines suggest that fame is temporary, ultimately resigned "To stillness and the alien stars".
One wonders if CAS' poem was a reflection on his own situation in 1941 (when he wrote "That Last Infirmity"), given that his generally formal, metrical style of poetry was out of fashion, and his period of writing fiction for commercial publication had come to an end.
It's always dangerous to read too much of the artist into the creative work itself, but fame was indeed headed in CAS' direction, since in 1942 Arkham House published a first collection of his stories, an event that would do a great deal to guarantee that CAS' writings would live on.