Hello
According to RFC-2131 section 4.3.4:
4.3.4 DHCPRELEASE message
Upon receipt of a DHCPRELEASE message, the server marks the network
address as not allocated. The server SHOULD retain a record of the
client's initialization parameters for possible reuse in response to
subsequent requests from the client.
When a router acting as DHCP server receives a DHCPRELEASE message it will not age-out an ARP entry for the leased IP address until the ARP timeout expires (default 240 minutes), or the IP is assigned to another end host which sends out a Gratuitous ARP message after accepting the IP, which effectively replaces the old entry in the ARP cache.
If you're asking about a layer 2 switch (e.g. a Catalyst) between the end host and the DHCP server, the switch will keep the MAC address in the switching table as long as Ethernet frames with that source MAC address are received on the port.
Best regards,
Martin