Hi there,

You may use below code. It will work accordingly 

<record model="ir.ui.view" id="partner_vendor_form_view">
    <field name="name">res.partner.with.buttonsfield>
    <field name="model">res.partnerfield>
    <field name="inherit_id" ref="base.view_partner_form"/>
    <field name="arch" type="xml">
        <data>
            
            <xpath expr="//field[@name='child_ids']/kanban/field[@name='name']" position="before">
                <field name="id"/>
            xpath>
            
            <xpath expr="//field[@name='child_ids']/kanban/templates//div[@class='oe_kanban_details']/field[@name='name']"
                   position="before">
                <a t-att-href="'#id='+record.id.raw_value+'&model=res.partner'"
                   class="fa fa-fw o_button_icon fa-external-link-square pull-right">
                a>
            xpath>
        data>
    field>record>

Note: I did that code in version 14 and its work properly. The only issue is you cannot move backward once you click on contact. it will open a separate view and the parent partner link will be disable