You use the history prop. You can read about it here: https://reacttraining.com/react-router/web/api/history
Essentially you wrap your component in the withRouter HOC, and it will pass the history prop to your component which you'll see here: https://reacttraining.com/react-router/web/api/withRouter. It blends very well with React Recompose. I modified the "basic example" of the react router docs as an example here of using withRouter with the history prop
// create-react-app test && cd test && npm i && npm install react-router-dom
// replace contents of App.js then `npm run start`
import React, { Component } from 'react';
import { withRouter } from 'react-router'
import {
  BrowserRouter as Router,
  Route,
  Link
} from 'react-router-dom'
class BasicExample extends Component {
  render() {
    return(
      <Router>
        <div>
          <ul>
            <li><Link to="/">Home</Link></li>
            <li><Link to="/about">About</Link></li>
          </ul>
          <hr/>
          <Route exact path="/" component={withRouter(Home)}/>
          <Route path="/about" component={About}/>
        </div>
      </Router>
    )
  }
}
class Home extends Component {
  render() {
    const {history} = this.props;
    const handleClick = (e) => {
      history.push("/about")
    }
    console.log(history)
    return (
      <div>
        <h2>Home</h2>
        <button onClick={handleClick}>To about</button>
      </div>
    )
  }
}
const About = () => (
  <div>
    <h2>About</h2>
  </div>
)
export default BasicExample;
If you're creating the link in your JSX, use the Link component, which looks like this
<Link to="/">...</Link>
If you're doing it inside of your PrivateRoute component, I think what you want is something more like the Redirect component: https://reacttraining.com/react-router/web/api/Redirect
  const PrivateRoute = ({ component: Component, ...rest }) => (
    <Route {...rest} render={props => (
      props.isAuthorized ? (
        <Component {...props}/>
      ) : (
        <Redirect to={{
          pathname: '/',
          state: { from: props.location }
        }}/>
      )
    )}/>)