"The Cow" milk/ilk rhymer (4)
I believe the answer is:
nash
(Other definitions for nash that I've seen before include "Famous dandy, Beau --" , "English architect, d. 1835 - American poet, d. 1971" , "Marble Arch designer" , "Ogden --, US humorous poet" , "English architect, d. 1835 - English war artist, d. 1946" .)