
A sleuth is a detective: most often, the word is used to describe an amateur or privately employed detective rather than a police officer. As a word, it was very popular in early detective fiction such as that written by Sir Arthur Conan Doyle or Agatha Christie, and is perhaps less popular now than in previous generations. Even so, it it is a word with a fascinating history.
As a keen reader of mystery fiction for many years now I am familiar with many sleuths. I started with Tricia Belsen, the Hardy Boys and the like. Scooby Doo and the gang were my favourite TV sleuths, but my parents loved Jessica Fletcher. As an adult, Sherlock Holmes, Miss Marple, and Phryne Fisher rank among my favourites. As much as I love Agatha Christie’s work, I always found Hercule Poirot to be insufferably smug and somewhat condescending, but that is a different discussion.
Sleuth had come into English at some point before 1200 AD, meaning ‘a definite track or trail left by someone or something’. This came from the Old Norse word sloð which means trail. This word was used to describe dogs skilled at tracking and following a scent or trail, known as sleuth-hounds. Thus, the first sleuths were not people, but dogs!
Eventually, the word came to be used for a person who tracked prey, or fugitives, or anything else in need of finding. It was used as a noun for a keen investigator by the mid 1800s, and for someone looking for clues to solve a crime in 1872. “detective” is 1872, shortening of sleuth-hound “keen investigator” (1849), a figurative use of a word that dates back to late 14c. meaning a kind of bloodhound.
Sleuth was not used as a verb until the early 20th century, when it was used to mean the act of investigating. The first written record of sleuth as a verb was in 1905. To sleuth out meant to investigate or discover, and the act of doing so was sleuthing.

Sources:
Etymonline
Sesquiotica
The Word Detective
Sleuth.
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