The honest answer leads with a hard truth and then the genuine hopes, because overwritten is a stronger word than deleted and shapes everything:

The hard truth about overwritten specifically: truly overwritten data, where new footage was physically written over the old on the same disk sectors, is generally not recoverable, since recovery works by finding data still physically present but unindexed and overwriting replaces the physical data itself. A CCTV loop that has genuinely recorded over the date you need has, in the worst case, replaced those bytes. This is different from deleted, and the distinction is why CCTV footage past the loop is often the one genuinely hard recovery.

The real hopes, since worst case is not always the case: partial overwriting, since the loop may not have overwritten every sector holding your footage, especially if the footage you need is recent relative to the loop cycle, meaning a recovery tool scanning the DVR drive may find fragments or whole segments not yet overwritten. Stop recording immediately, power the system down or set it to not overwrite, since every hour of continued recording overwrites more, the single most important action and the one most often missed while people investigate.

The recovery attempt itself: the DVR drive removed and connected to a computer, then scanned with video recovery tools or a professional service that understands the DVR's proprietary recording format, since CCTV systems often use non standard filesystems that generic tools misread. A professional data recovery service experienced with CCTV is the realistic route for footage that matters, an incident or legal need, rather than consumer tools against a proprietary format.

The action priority given a real need: stop the overwriting now, before anything else, since the footage's survival depends entirely on not writing more, then engage professional recovery with the drive rather than experimenting, since amateur attempts on a proprietary DVR filesystem can worsen the odds. The uncomfortable prevention lesson for the future is a longer retention loop or offloading important footage before the loop reaches it, since the loop overwriting needed footage is the system working as configured rather than a fault.