App.js

const [express, compression] = [require('express'), require('compression')];
const [app, router] = [express(), express.Router()];

app.use(compression());




app.get('/', router);
router.get('/', (req, res) => {
    res.status(200).send({messge: 'compressed response'})
});

app.listen(4000, () => {
    console.log('server start');
});

compress npm

You could configure it the server. Before that, you need to know which web server you use. It can be nodejs, nginx, apache etc

But instead of doing that in your server, I would suggest giving that work to Cloudflare. They'll take care of it. They also use brotli (better than gzip) whenever possible

Compressing the API response is the role of your web server. What software your server runs on? For instance, if it is Node.js you can use compression module to achieve gzip compression.