I was absent when the midterms were handed back for a course
This is not the fault of your instructor.
I need the midterm to study for the exam
You would like a copy of the midterm to study; you do not need it.
The exam is in a week from now
Presumably, you knew there would be a final exam when the course started, so this is not new information to you. Therefore the timing and the inability of your professor or TA to obtain your exam in that short time is not their fault.
Would it be helpful to for example contact the department chair or someone in authority even though there may be no obligation to return the exam or send a scanned copy?
No, I do not think that would be helpful, I think that would be incredibly rude. You are in a situation of your own making. You have a want, not a need, for access to your previous exam, which you are expressing far later than you should have if you thought this was necessary. There is a oft-repeated phrase that addresses this situation: "Poor planning on your part does not necessitate an emergency on mine."
I don't think your professor or TA are doing anything intentionally to prevent you from accessing the exam. It seems that the copy of your exam, likely the only copy, is simply not in a location that either of them can access before your final exam, which is not surprising given the compressed time frame until your final, and the long time elapsed since the midterm.
I think it would be reasonable to let your professor know that the TA was unable to access your exam in time to help you study, and to ask instead for a fresh copy of the midterm, and perhaps note that you'd appreciate an answer key, too, if available. I think it's fine to CC your TA, too. It's more likely one of them has an easily-accessible copy of a drafted exam than your specific copy. I would recommend an attitude of appreciation for whatever they are able to obtain for you, and appreciation for their efforts to try to help even if they are unable.