A syringe was an instrument used to administer drugs or apply liquids in controlled amounts.
The First Doctor used a syringe of prussic acid to kill a Zilgan on the Sense Sphere. (PROSE: The Monsters from Earth)
Tasambeker killed Jobel by injecting him in the heart with a syringe filled with green liquid. (TV: Revelation of the Daleks)
The Seventh Doctor used a syringe filled with maxenshudicea to save the Culture from an invading virus. (COMIC: Culture Shock!)
Dalek Jast of the Cult of Skaro had a syringe attachment on their manipulator arm in place of the plunger. (TV: Daleks in Manhattan)
Danny used a syringe to administer insulin to himself to treat his diabetes. He offered his syringe to inject Jack Harkness with EDTA and cure his cyanide poisoning, saying that his diabetes "finally comes in handy". (TV: Rendition)
At some point in Earth's history, syringes were replaced by air injectors, which were entirely painless. (AUDIO: The Rise of the New Humans)