Set DNS servers for DHCP clients?

> Is there a way to specify the DNS server that the Netgear gives to DHCP
> clients? [...]

   I've never seen a consumer-grade Netgear router which offered any
supported way to change such DHCP parameters.  Lease time is another one
which appears in requests from time to time.

   The usual suggestion is to run another DHCP server (perhaps on a
Raspberry Pi?), and disable the one on the Netgear router.

> [...] At present DHCP clients get the cable providers DNS servers, a
> 208 subnet. [...]

   They do?  I don't see how.  I'd expect any Netgear router to offer
itself as the DNS server; otherwise the "routerlogin" names couldn't
work.  (The Netgear router would forward normal DNS requests to the DNS
server(s) specified in its BASIC > Internet settings, which might or
might not be your ISP's DNS server(s).)

> [...] Is there a need to specify the router. or is it implied somehow,
> even if the DHCP server doesn't specify the router?

   You lost me.  I don't know what that means.