Whether you need a licence will depend on how the image is being used.
The Premier League owns the copyright on static shots of the trophy and you must request permission from the Premier League to use it in the first instance.
If permission is granted, it is important to note that all trophy imagery must be used in its original form and in its entirety, must not be changed or manipulated in any way and must always include the ribbons incorporating the title sponsor's name and the approved competition title as well as the correct club colours of the most recent winners of the competition.
Images showing a more dynamic version of the trophy, held aloft with flowing ribbons for example are unfortunately not available from the Premier League.
Any such images would need to be sourced from an official photographic licensee such as Action Images (actionimages.com).