Ape-leader is an archaic English idiom for an old maid, that is, a woman past marrying age who has never been married.
This is quite a bit more rude than it sounds. It does not refer to the person's looks, but the fact that they will go to hell for not marrying. It comes from a common folk saying that appeared around the time of the English Reformation, c. 1560: "Such as die Maydes, doe all lead Apes in hell" (Samuel Rowlands, 1602).
This is generally understood to be punishment for not following the godly command of "go forth and multiply", and suffers from a double-meaning that may not be apparent to modern readers, as 'lead' was also an euphemism for flirting and/or having sex with someone. Shakespeare, of course, was happy to take advantage of this, and used the phrase in a couple of plays (The Taming of the Shrew, Much Ado About Nothing, and The London Prodigal) to bawdy effect.
The first appearance that I have found of the phrase 'ape-leader' in the wild is in Colley Cibber's play Lady's Last Stake (1707); it appears in writing almost entirely in the context of plays and slang dictionaries until the 1900s, when it was popular slang in romantic Regency novels. It most likely fell out of popular use in the late 1800s, thereafter regulated to historical fiction; as it appears in many historical slang dictionaries, it is oft-used in those works.
Ape-leader is traditionally hyphenated, but despite no one using this phrase for the last hundred years, there is a trend in modern dictionaries to update it forgoing the hyphen.