61.39(b) Notwithstanding the provisions of paragraphs (a)(1) and (2) of this section, an applicant for an airline transport pilot certificate ... may take the practical test for that certificate or rating with an expired knowledge test report, provided that the applicant:
(1) Is employed as a flight crewmember by a certificate holder under part 121, 125, or 135 of this chapter at the time of the practical test and has satisfactorily accomplished that operator's approved--
(i) Pilot in command aircraft qualification training program ...and
(ii) Qualification training requirements appropriate to the certificate and rating sought; or
[(2) Is employed by the U.S. Armed Forces as a flight crewmember in U.S. military air transport operations at the time of the practical test and has completed the pilot in command aircraft qualification training program that is appropriate to the pilot certificate and rating sought.]

So the answer is, it depends. If you have an "old" written and are upgrading through the training program of an air carrier that you work for you're covered. If you work for an air carrier but decide to upgrade on your own outside of work you'll need a current written. And if you you don't work for an air carrier you'll need a current written.