An expired flight instructor certificate may not be renewed, but must be reinstated (See 14 CFR 61.199). Either a designated flight instructor, or an aviation safety inspector may accomplish the practical test to reinstate a flight instructor certificate.
However, a designated pilot examiner must have authorization to grand flight instructor privileges; not all DPE's can do this.
To reinstate flight instructor privileges, all requirements for the origional issuance of the certificate must be met.
FAA Order 8400.10 (Air Transportation Operations Inspector's Handbook), Volume 5, Chapter 9, Section 6, Para 773:
773. EXPIRED CERTIFICATES. The procedures described in this section shall not be used to reinstate an expired flight instructor certificate. An applicant for reinstatement of an expired flight instructor certificate may exchange that certificate for a new certificate by passing the practical test prescribed in FAR 61.187. That practical test shall be administered by either an appropriately rated operations inspector or an appropriately designated pilot examiner.