roooter.js

// services/router.js

import Router from '@ember/services/router' // or wherever it lives
import Evented from '@ember/evented'

export default Router.extend(Evented);

// your helper

export default Helper.extend({
  router: service(),

  init() {
    this._super(...arguments);
    this._fn = () => this.recompute();
    this.get('router').on('didTransition', this._fn);
  },
  
  willDestroy() {
    this.get('router').off('didTransition', this._fn);
  },
  
  compute() {
    // magic here
  }
});

// application/route.js

export default Route.extend({
  router: service(),
  
  actions: {
    didTransition() {
      this.get('router').trigger('didTransition');
      return true;
    }
  }

});