Some games may have audio blocked due to copyright/legal/Sony-being-retarded issues. If even system audio is not present, check your settings in Elgato control panel and make sure the device is setup to encode audio as well as video. The audio should be sent directly to your audio panel in OBS when the device is added, but if for some reason it isn't, then open device properties and enable audio there.
Disable HDCP (High-bandwidth Digital Content Protection) on the PS4 settings. You may not be able to use services such as YouTube or Spotify after doing so.
Also make sure your volume is turned on. You'd be surprised by how many people forget to do this...
If you have your audio being sent through your controller/headset... don't. You can't capture audio unless it's being sent through your HDMI/digital output.
A word of advice: The HD60 is garbage in terms of hardware. The gate arrays and Asics in the card is very unstable, only USB 2.0 support, and the built-in encoder has poor performance, very low efficiency as well as no "fast-decode" support and occasional framedrops. Try other capture cards if you can still return it. Same with the turtle beach headsets. The drivers in those headsets are very low quality, with a narrow frequency response (20-20khz) given the size of the headset. The microphone also only has a thin widescreen with no pop filters. I would advise that you return it although that's up to you, as it is a decent headset considering the very low price. I recommend the Sennheiser HD1 Wireless ($500) if you can afford it. The elgato HD60 pro ($200) a good cheap solution for recording PS4 and other standard outputs. If you want 4k outputs, the Matrox Mura IPX ($5000-10000) is a very nice capture card capable of recording 4k at 32 bit color depth.
