It’s all a bit hazy what will happen.
If the deal is agreed, their is a transitional period until the end of 2020 and EU players will be able to still enjoy freedom of movement to the UK and thus won’t need a work permit.
If it is no-deal then it will be up to the FA and the Home Office what happens. The default position will be that all players that don’t hold an British or Irish passport will require a work permit. Currently the Home Office will give a work permit to any professional player, who earns over £42,000 a year if they obtain a Governing Body Endorsement (GBE), from the the FA. The FA current run a points based system to determine whether a player qualifies for the GBE. Points are awarded based on a set of criteria that takes international apperances, wages and transfer fee into account. If the FA don’t change their criteria then the amount of overseas players coming into the UK will dry up dramatically, the BBC did a study that found that over 300 players in the Premier League, Championship and SPL who signed on EU passports would not get a work permit.
How the FA react to a no-deal scenario will be interesting, they have been trying to crack down on overseas players and may see this as a good way to do so, although the Premier League will be furiously trying to get them to be more lenient.
The Government have said that EU citizens that are currently in the UK will have their rights protected, so that means players currently playing here won’t need to get a work permit to stay.
The summee transfer window could be insane, the shorter period that was brought in last year combined with clubs being unable to bring in the majority of European players will drive up the price of all UK players. People like Max Aarons could suddenly become worth £30m and command huge wages. It could be a very tough situation for Norwich as they will likely lose the ability to recruit smartly from Europe, which they have done excellently recently.