[Vuejs]-How to Add Icon in AG Grid Custom Header in vue js

because you’re rewriting ag-grid header with you’r custom one, and not adding the sorting and filtering in it

here is an example how it should look like:

export default Vue.extend({
template: `
<div>
  <div
    v-if="params.enableMenu"
    ref="menuButton"
    class="customHeaderMenuButton"
    @click="onMenuClicked($event)"
  >
    <i class="fa" :class="params.menuIcon"></i>
  </div>

  <div class="customHeaderLabel">{{ params.headerName }}</div>

  <v-tooltip  bottom max-width="200">
    <template v-slot:activator="{ on }">  
      <i v-on="on" class="custom-info info circle icon"></i>
    </template>
    <span>{{ params.toolTipText }}</span>
  </v-tooltip>

  <div
    v-if="params.enableSorting"
    @click="onSortRequested('asc', $event)"
    :class="ascSort"
    class="customSortDownLabel"
  >
    <i class="fa fa-long-arrow-alt-down"></i>
  </div>

  <div
    v-if="params.enableSorting"
    @click="onSortRequested('desc', $event)"
    :class="descSort"
    class="customSortUpLabel"
  >
    <i class="fa fa-long-arrow-alt-up"></i>
  </div>

  <div
    v-if="params.enableSorting"
    @click="onSortRequested('', $event)"
    :class="noSort"
    class="customSortRemoveLabel"
  >
    <i class="fa fa-times"></i>
  </div>
</div>
`;
data: function () {
    return {
        ascSort: null,
        descSort: null,
        noSort: null
    };
},
beforeMount() {},
mounted() {
    this.params.column.addEventListener('sortChanged', this.onSortChanged);
    this.onSortChanged();
},
methods: {
    onMenuClicked() {
        this.params.showColumnMenu(this.$refs.menuButton);
    },

    onSortChanged() {
        this.ascSort = this.descSort = this.noSort = 'inactive';
        if (this.params.column.isSortAscending()) {
            this.ascSort = 'active';
        } else if (this.params.column.isSortDescending()) {
            this.descSort = 'active';
        } else {
            this.noSort = 'active';
        }
    },

    onSortRequested(order, event) {
        this.params.setSort(order, event.shiftKey);
    }
}
});

example was taken from ag-grid documentation: https://www.ag-grid.com/javascript-grid-header-rendering/#vueCellEditing

also here https://www.ag-grid.com/javascript-grid-header-rendering/#vueCellEditing you could find more details related to how header components works and custom header components should work