This item is only of concern to English athletes.
What is EA? - England Athletics is the governing body which manages and develops Athletics in England, performing the same kind of duties as were performed by the AAA (and its regional bodies, e.g. NoEAA, SoEAA etc) in the past. Scottish Athletics, Welsh Athletics and Athletics Northern Ireland are the equivalent bodies in the other home nations. EA licenses many athletics events, including road races, in the same way that the FRA licenses fell races. They have an affiliation scheme for clubs, and charge their clubs a levy of £10 per year to register each individual athlete.
Other reasons to register - You can take part in other types of races (e.g. road races) without paying the EA supplement (normally £2 per race). If you want to race abroad, you can often use your EA Competition Licence instead of paying for a doctor's "fitness-to-race" letter.
Can I register with EA via the FRA – This is no longer possible. To get EA registration you should join a club which is affiliated to England Athletics, and pay the registration fee as part of your club subscription. Most fell-running clubs are affiliated to EA, or otherwise you will need to join an EA-affiliated road running or athletics club in addition to any fell-running club.