If your domain transfer was initiated before the the expiration date, the transfer can still be completed. Most domain registrars will let the domain transfer continue if the domain has expired before the transfer has been completed, however, there are a few registrars that will manually deny the transfer after the domain has expired. If this worries you, you should contact your previous domain registrar, and ask them if they will still let the domain transfer continue since the transfer was initiated before the domain expired.
Please note that a domain transfer does not start right after you submit a domain transfer order to us. A domain transfer starts after the transfer has been authorized. You will receive a "Transfer Initiated" email from us when that happens.