Do I Have to Change the Name Servers at My Old Host Before I Transfer My Domain Registration?
Although it is not required, it is a good idea to update the name servers to the HostGator name servers prior to initiating transfer to avoid any downtime.
Once you initiate the domain registration transfer process, you will not be able to update the WHOIS information or the name servers until the process is complete. The transfer process can take up to seven (7) days to complete, so please allow plenty of time for your previous registrar to approve the transfer.
For further information about transferring domains and changing name servers, please review the following article: