Extended metaphors are, not surprisingly, metaphors which are continued at length. They were much admired in classical writing (in Latin and Greek, and in English by those who admired the ancient styles.) There are also extended similes, which often begin, in neo-classical English verse, with the words "As when ..." (~ "This is like the time[s] when ...").
Some poems are based on a single extended metaphor. The American poet e.e. cummings (sic) wrote a poem ("she being Brand/-new") which is all about driving a new car for the first time, but is also about the first act of love with a new lover.