It depends on how big your Time Machine backup is. As noted by Bigwaff, older backups are deleted as space is required, but if you have a larger drive, the further back your TM will be able to go before deletions happen.
But unless there's a software / hardware issue, while your drive may look like its getting full, the app should maintain space for recent backups.
As a sidebar to this (not affecting your external drive but your Mac's internal one) there may be occasions where your TM wasn't able to access your external drive for whatever reason at the appointed time. If that's the case, it will save the backup to your Mac's internal drive. These may add up over time, taking valuable storage space. You can see if these exist by opening Terminal and typing -
tmutil listlocalsnapshots /
- then hit Return key. It will either tell you none exist, or list them. If you wish to delete them, type -
tmutil deletelocalsnapshots /
- then hit Return key.