Inside the app go to the menu More and scroll down to Advanced Audio Settings toward the bottom. Tap on the blue dot under "Custom audio buffer size" and drag it to the right to increase the buffer size.
This should improve the sound, however, results will vary depending on your device.
OS 4.4 to 8.3:
In iReal Pro, tap on More and scroll down to the Audio settings. There is an Open SL audio switch which improves the audio quality on certain devices.