奏 is used in formal/classical music contexts. Key compounds: 演奏 (to perform music), 节奏 (rhythm/tempo), 独奏 (solo), 合奏 (ensemble). In daily life, 弹 (tán, for piano/guitar) and 拉 (lā, for violin) are more common for 'playing an instrument.'
history
In ancient China, 奏 also meant to present a report to the emperor — 奏折 (zòuzhé, memorial to the throne). This meaning survives in historical dramas.