ST_LongestLine

ST_LongestLine(geom1: Geometry, geom2: Geometry)

SELECT ST_LongestLine(
        ST_GeomFromText("POLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))"),
        ST_GeomFromText("POLYGON ((10 20, 30 30, 40 20, 30 10, 10 20))")
)

LINESTRING (40 40, 10 20)