Macbook Pro early 2007 SSD to the new Macbook Air 2017 install?
Your "old"ssd has a sata connector, while the MBA has a pcle connector. Aso the old SSD is much larger than the one inside the MBA. In short: no way.
But you can insert an SD card and format that as GUID, Mac OS extended (journaled)as a storage expansion.
here is an Apple article that describes the slot:
https://support.apple.com/en-us/HT204384
and here is an article that describes the uses for the SD slot:
https://www.macworld.com/article/3329753/macs/older-mac-sd-card-slot.html
Altogether an easy and cheap solution for your "problem".