partner-contact/animal_owner/views/res_partner.xml

<odoo>

    <!-- Partner Form View -->
    <record id="view_partner_animal_owner_form" model="ir.ui.view">
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_partner_form" />
        <field name="arch" type="xml">
            <div name="button_box" position="inside">
                <button
                    class="oe_stat_button"
                    type="object"
                    name="action_view_animals"
                    icon="fa-pencil-square-o"
                    context="{'default_partner_id': id}"
                >
                    <div class="o_stat_info">
                        <field name="animal_count" class="o_stat_value" />
                        <span class="o_stat_text"> Animals</span>
                    </div>
                </button>
            </div>
        </field>
    </record>

</odoo>