If your visit to the United States is outside of the date you have left on your current ESTA, you will have to re-apply on the ESTA U.S Department of Homeland Security website, which is here....
https://esta.cbp.dhs.gov/esta/of
The website that has sent you the reminder appears to be legit, but I personally wouldn't trust them, and they will charge you a payment for using their service.
On the legitimate website i have sent you, you'll only pay the processing fee of US $4 dollars and, when authorised, additional US $10 dollars, which you can pay by card, which will convert the payment into £ Sterling.
Have a great trip, tearinghair