When you start recording a CD-R you open a session and when the recording ends, the disc is "closed" meaning no more data can be added to the CD-R. The unused space is unavailable and "invisible" for the player.
Your burner software must have a "multisession" option that let you record a session and keep the unused space available for a new session.
During the late 90s and early 2000s, some record labels sold multisession CDs, one having the audio tracks and other with video and multimedia content.