Anaesthetic

An anaesthetic was a kind of liquid or gaseous drug, able to sedate living beings, used on Earth and other planets.

Earth
It was used by staff of Walker General Hospital on the Seventh Doctor in the operating theatre when he went in for emergency heart stabilising surgery. The Doctor awoke from pre-op sedation by Madame Butterfly, and the anaesthesiologist used it to put the Doctor under. The Doctor died while anaesthetised, which delayed the regeneration process. The regeneration process came hours after the death, aggravated with a temporary amnesia; the Eighth Doctor ascribed such side effects to the anaesthetic. (TV: Doctor Who)

In 2700 BC Mesopotamia, Ishtar used ether as an anaesthetic. (PROSE: Timewyrm: Genesys)

Anaesthetic darts were developed by MI6 for operatives to use in the field. (TV: Spyfall)

Extraterrestrial uses
employed sleeping gas in the alarm system of his TARDIS. It was scattered in the console room after the Third Doctor had stolen its dematerialisation circuit. (TV: Colony in Space)

On Karn, the human surgeon Solon shot the fresh-revived and violent Morbius with an anaesthetic. (TV: The Brain of Morbius)

On Alzarius, chief scientist Dexeter administered anaesthetic to a Marshman in order to sedate and vivisect him. (TV: Full Circle)

The biogeneticist Dastari couldn't give a full anaesthetic to the Second Doctor during the operation for extracting his symbiotic nuclei, because he had to be conscious during the "neuron bombardment". The scientist injected him a simple inhibitor of the motor centres. Nonetheless, the Doctor was asked to count backwards to ten and, eventually, passed out. (TV: The Two Doctors)