Align search bar and button once clicking on search icon

I hope you are well today and thank you for your question.

Could you please share me your site URL where it’s displaying so that I can help you to achieve it?

Best regards,
Ivory Search Support

Yes, the Ivory Search plugin needs to enable as without enabling it I can’t see the search form on your site.

After enabling it, you can just hide it for your site users so that it won’t display broken by adding the below CSS code in the Custom CSS option of Ivory Search plugin settings on the path Ivory Search -> Settings -> Settings

.is-menu {
display: none !important;
}

You can achieve this by removing the above shared CSS code and using below CSS code.

#mega-menu-wrap-main-nav .is-menu input.search-field {
    float: left;
    margin: 0;
}

#mega-menu-wrap-main-nav .is-menu .search-submit {
    padding: 11px 10px;
    min-width: 0;
    font-size: 14px;
    float: left;
    height: auto;
    line-height: 14px;
    margin: 0;
}

#mega-menu-wrap-main-nav .is-menu  .search-close {
    top: 38px;
    right: 8px;
}