Macbook Pro early 2007 SSD to the new Macbook Air 2017 install? I would really appreciate your advice on this matter.

I have a macbook pro early 2007. Its old i know and last year i replaced the HDD with a 420GB SSD as the HDD failed. It was a fairly straightforward install.

However, physically it is falling to bits and the screen casing is broken. Still runs fine though.

SO my generous girfriend has bought me a new Macbook air pro 13 inch 18ghz, 8gb, 128gb laptop. Initially i was delighted about this but i have something of a quandary.

The HD is only 128gb in the macbook air. No where near enough the space i need on a computer. My music collection alone is this. 

The bottom line is, can I take out the 420GB SSD drive in my old mac running El Capitan and simply install it in the new Macbook air?

In theory it sounds easy, replace the hard disk, startup the new Air computer and then update the OS to the latest one as the old mac only goes up to capitan.

Any advice greatly appreciated.

Many thanks
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".