vue-select/docs/.vuepress/components/ValidationRequired.vue

<template>
  <form @submit.stop="onSubmit">
    <v-select :options="books" label="title" v-model="selected">
      <template #search="{attributes, events}">
        <input
          :required="!selected"
          class="vs__search"
          v-bind="attributes"
          v-on="events"
        />
      </template>
    </v-select>

    <input type="submit">
  </form>
</template>

<script>
import books from '../data/books'
export default {
  data: () => ({
    books,
    selected: null,
  }),
  methods: {
    onSubmit() {
      alert('Submitted!');
    }
  }
};
</script>

<style scoped>
  form {
    display: flex;
    align-items: stretch;
  }

  .v-select {
    width: 75%;
  }

  input[type="submit"] {
    margin-left: 1rem;
    background: #44ae7d;
    border: none;
    border-radius: 3px;
    color: #fff;
    width: 20%;
  }
</style>