This example uses OpenLayers v10.9.0. The latest is v.
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#### Vector tiles reprojected

vectortiles 6 tile 10 mapbox 8 maplibre 1 ol-mapbox-style 3 reprojection 8

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Example showing vector tiles in EPSG:4326, reprojected to a polar projection.

Vector tile layers can be reprojected to other projections. This example shows vector tiles in geographic coordinates (EPSG:4326) reprojected to North Pole Lambert Azimuthal Equal Area (ESRI:102017). For polar regions, vector tiles in geographic coordinates are recommended, because Web Mercator tiles do not work beyond 85° North and South.
Note: Make sure to get your own API key at https://www.maptiler.com/cloud/ when using this example. No map will be visible when the API key has expired.

##### main.js

    import {applyBackground, applyStyle} from 'ol-mapbox-style';
    import Map from 'ol/Map.js';
    import View from 'ol/View.js';
    import VectorTileLayer from 'ol/layer/VectorTile.js';
    import {fromLonLat} from 'ol/proj.js';
    import {register} from 'ol/proj/proj4.js';
    import VectorTileSource from 'ol/source/VectorTile.js';
    import {createXYZ} from 'ol/tilegrid.js';
    import proj4 from 'proj4';

    // Register proj4 definition for North Pole Lambert Azimuthal Equal Area
    proj4.defs(
      'ESRI:102017',
      '+proj=laea +lat_0=90 +lon_0=0 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs +type=crs',
    );
    register(proj4);

    const key = 'Get your own API key at https://www.maptiler.com/cloud/';
    const url = 'https://api.maptiler.com/maps/basic-4326/style.json?key=' + key;

    const layer = new VectorTileLayer({
      declutter: true,
      source: new VectorTileSource({
        projection: 'EPSG:4326',
        // Match the server resolutions
        tileGrid: createXYZ({
          extent: [-180, -90, 180, 90],
          tileSize: 512,
          maxResolution: 180 / 512,
          maxZoom: 13,
        }),
      }),
    });
    applyStyle(layer, url);
    applyBackground(layer, url);

    const map = new Map({
      target: 'map',
      layers: [layer],
      view: new View({
        projection: 'ESRI:102017',
        minZoom: 3,
        zoom: 4,
        center: fromLonLat([0, 90], 'ESRI:102017'),
      }),
    });

##### index.html

    <!DOCTYPE html>
    <html lang="en">
      <head>
        <meta charset="UTF-8">
        <title>Vector tiles reprojected</title>
        <link rel="stylesheet" href="node_modules/ol/ol.css">
        <style>
          .map {
            width: 100%;
            height: 400px;
          }
        </style>
      </head>
      <body>
        <div id="map" class="map" style="background:none;"></div>

        <script type="module" src="main.js"></script>
      </body>
    </html>

##### package.json

    {
      "name": "vector-tiles-reprojected",
      "dependencies": {
        "ol": "10.9.0",
        "ol-mapbox-style": "^13.4.1",
        "proj4": "2.20.8"
      },
      "devDependencies": {
        "vite": "^3.2.3"
      },
      "scripts": {
        "start": "vite",
        "build": "vite build"
      }
    }