Playing a flute
A fife, a type of simple flute
The flute was a small wind instrument, typically made out of metal or wood.
Jenna D'Sora of the USS Enterprise-D played the flute. (TNG: "In Theory")
Captain Jean-Luc Picard played the Ressikan flute. (TNG: "The Inner Light", "Lessons")
When Miles O'Brien was having troubles with a Cardassian vole infestation on Deep Space 9, Doctor Julian Bashir gave him a small metal fife in a box and left a note, stating "It worked in Hamlin". (DS9: "Playing God")
While stranded on Dilmer III in 2382, Lieutenant jg Beckett Mariner carved a flute from soap in an attempt to emulate Picard's experience on Kataan. However, the flute sounded terrible and she did not play it skillfully, so she threw it away in frustration and it broke. (LD: "Fully Dilated")