In the python file

from odoo import models,fields,api
class ResPartner(models.Model):
_inherit = 'res.partner'
postal_code = fileds.Integer(string="Postal Code")

In the xml file

<odoo>
    <record id="partner_inherit_postal" model="ir.ui.view">
    <field name="name">partner.postal.code.inherit</field>
    <field name="model">res.partner</field>
    <field name="inherit_id" ref="base.view_partner_form"/>
    <field name="arch" type="xml">
        <xpath expr="//field[@name='zip']" position="replace">
            <field name="postal_code"/>
        <xpath>
    </field>
</record>
</odoo>

You get the basic idea..