A syringe was a medical device used to inject small amounts of drugs or to take blood samples.
Syringes were in use on Earth for many centuries but were no longer used in the 24th century, when hyposyringes and hyposprays were employed instead.
Nurse Faith Garland injected Quark with Sodium Pentathol by means of a syringe. (DS9: "Little Green Men")
The Ferengi still used traditional syringes. Doctor Arridor used a syringe to take a sample of DaiMon Goss' blood pyrocytes. (TNG: "The Price")