Expanding up or down
As there is only two states, up and down, we can leave out .expand-up and let it be the default state. I refactored the css and js code to just add and remove the expand-down class, for the .css file,

body {
    font-size: 62.5%;
    font-family: 'Roboto', sans-serif;
    color: #FFF;
}
.filter-search {
    background-color: #a78464;
}
.filter-search .wrapper {
    width: 100%;
    text-align: center;
    height: 10em;
    transition: height linear 1s;
}
.filter-search .wrapper .title-wrapper {
    display: inline-block;
    animation-fill-mode: forwards;
    animation-duration: .5s;
    -webkit-animation-fill-mode: forwards;
    -webkit-animation-duration: .5s;
}
.filter-search .wrapper .title-wrapper.expand-down {
    -webkit-animation: moveDown ease-out 1;
    animation: moveDown ease-out 1;
}
.filter-search .wrapper .title-wrapper h2 {
    font-size: 3em;
    margin-bottom: 0;
}
.filter-search .wrapper .title-wrapper span {
    font-size: 1.4em;
    display: block;
    text-transform: uppercase;
    margin-bottom: 2em;
}
.filter-search .wrapper.active {
    height: 15em;
    transition: height linear 1s;
}
@-webkit-keyframes moveUp {
    0% {
        margin-top: 0;
    }
    to {
        margin-top: -1em;
    }
}
@keyframes moveUp {
    0% {
        margin-top: 0;
    }
    to {
        margin-top: -1em;
    }
}
@-webkit-keyframes moveDown {
    0% {
        margin-top: -1em;
    }
    to {
        margin-top: 0;
    }
}
@keyframes moveDown {
    0% {
        margin-top: -1em;
    }
    to {
        margin-top: 0;
    }
}


and for the .js file I changed click() to on(), in case the element will be added dynamically, click() would not work. Also assigning variable filterSearch earlier in the function, there should be no need to find the children with each click,

$(document).ready(function() {
    $('#filter-search').on('click', '.title-wrapper', function() {
        var filterSearch = $(this);

        filterSearch.parent().toggleClass('active').delay('1500').promise().done(function() {
            if (filterSearch.hasClass('expand-down')) {
                filterSearch.removeClass('expand-down');
            } else {
                filterSearch.addClass('expand-down');
            }
        });
    });
});