To override a search component and add your own search experience, you will have to implement forceCommunity:searchInterface. The sample code snippet is as follows:

<aura:component implements="forceCommunity:searchInterface" access="global">
    <div class="search">
        <div class="search">
            <form class="search-form">
                <div class="search-input">
                    <input class="search-input-field" type="text" placeholder="My Search"/>
                </div>
                <input type="hidden" name="language" value="en" />
            </form>
        </div>
    </div>
</aura:component>