How to deal with a lazy postdoc colaborator as a PhD student?
Sometimes, when the expected first author of a publication abandons it, one of the others steps up to becoming the driving force behind the writing. If you understand the project well enough and care enough about the writing, that person might be you. 

If you want to do this, you first need to talk to your supervisor and have them talk with the other supervisor. If they agree with the plan, then you don't have to wait for the non-writing author any more, but can go ahead with working on the writing yourself. Authorship order might or might not end up changing, but at least you'll be much more likely to end up with a paper.

Alternately, not all papers that are started get completed.  If it is not important enough to you to invest that level of time and effort, this might be one of those for you, and you may need to move on to completing and writing up your next project.