How to increase the height of column header in ag-grid?

You can add run-time also according to header content using grid api:

onGridReady(params) {
    this.gridApi = params.api;
    this.gridApi.setHeaderHeight(<set your header height in pixel>);
}

bind onGridReady() function to gridReady event as follows:

<ag-grid-angular(gridReady)="onGridReady($event)"> </ag-grid-angular>

Header Height property can also be set directly on the grid component in pixels like so:

<ag-grid-vue style="width: 100%;height: 47vh;"
    class="ag-theme-balham"
    :columnDefs="columnDefs"
    :rowData="rowData"
    headerHeight="50">
</ag-grid-vue>

check Column Headers documentation https://www.ag-grid.com/javascript-grid-column-header/

two options

1- properties that can be used to change the different heights

<ag-grid-angular
    [columnDefs]="columnDefs"
    [rowData]="rowData"
    [headerHeight]="headerHeight"
    [groupHeaderHeight]="groupHeaderHeight"
    [floatingFiltersHeight]="floatingFiltersHeight"
    [pivotGroupHeaderHeight]="pivotGroupHeaderHeight"
    [pivotHeaderHeight]="pivotHeaderHeight"
></ag-grid-angular>

2- setter methods that can be called from the API

<ag-grid-angular
    [columnDefs]="columnDefs"
    [rowData]="rowData"
    (gridReady)="onGridReady($event)"
 ></ag-grid-angular>

onGridReady(params) {
    this.gridApi = params.api;
    this.gridColumnApi = params.columnApi;
}

setHeaderHeight(value) {
    this.gridApi.setHeaderHeight(value);
    setIdText('headerHeight', value);
}

setGroupHeaderHeight(value) {
    this.gridApi.setGroupHeaderHeight(value);
    setIdText('groupHeaderHeight', value);
}

setFloatingFiltersHeight(value) {
    this.gridApi.setFloatingFiltersHeight(value);
    setIdText('floatingFiltersHeight', value);
}

setPivotGroupHeaderHeight(value) {
    this.gridApi.setPivotGroupHeaderHeight(value);
    setIdText('pivotGroupHeaderHeight', value);
}

setPivotHeaderHeight(value) {
    this.gridApi.setPivotHeaderHeight(value);
    setIdText('pivotHeaderHeight', value);
}