The original meaning of the phrase "old hat" as in "something considered to be old-fashioned, out of date, unoriginal, or hackneyed" was....
Vulva.
According to the OED, at least.
They have a hilarious citation from 1796 (which they dismiss as facetious rather than genuine etymology, the spoilsports):
1796
Old hat; a woman's privities: because frequently felt.
F. Grose, Classical Dictionary of Vulgar Tongue (1963) at Hat
This one is interesting too:
1980
'Tis a Nest, a Niche, an Old Hat, an Omnibus, an Oyster, a Palace o' Pleasure.
E. Jong, Fanny i. xv. 120
Omnibus? I say!