Hi,

Use the following code for adding the button in chatter

<t t-extend="mail.chatter.Composer">
    <t t-jquery=".o_composer_send" t-operation="after">
        <div class="col-lg-4">
            <button class="btn btn-primary" style="margin-top: 10px;"
                type="button">
            Button Name
            </button>
        </div>

    </t>
</t>

You can write the JavaScript code for adding functionality for the added button

Regards