Hi,
If you feel you need more fields to the partner form, you can add those new fields using Odoo studio if you are using Odoo enterprise. If you are using the community edition you can add those new fields by editing the original code or you can create a custom module for this.

Creating a custom module is preferred over editing the source code. Also, you can add fields from the user interface also, for that you can have a look at this video: https://www.youtube.com/watch?v=ZZwRvP7lJng

For creating a custom module read this blog: https://www.cybrosys.com/blog/how-create-module-odoo

Also,  you can refer this link to add a new field in existing model:  https://www.odoo.com/forum/help-1/question/extend-an-existing-model-by-inheriting-another-131340

Thanks