If they own the trademark (unlikely) your on thin ice, If there are three other clubs with the same and probally many people business also they would find it very very hard to try and win the domain of you.
If not you do not need there permission, They are not any different to any other business, If they are limited company then they have an obligation too share holders to maximise profits etc so they will not want you taking away possible revenue and would be very unlikely to grant you any permission and would want payment and if they did, would also want to have control over what you allowed on there because of sponsorship deals etc
You’ll see the web has 1000s of them Chelsea Liverpool mun utd etc cant stop them. Some very crafty people have even been known to buy a single share in a club/ business and used it to voice the opinion of the shareholder all perfectly legal
I would not contact them because if they say no very likely try and use you’re asking them against you?
A1 they could protest but it don't mean fiddly
A2 if any of them had a valid claim to the name they would be most likely to win it
A3 any name you register has the potential for legal action,You have to worry more about what you put on it than the name ?
(if your regged it recently and the club had not it’s very likely they did not want or knew they would not have a stong case to keep it reference the other, most clubs should be pretty clued up when it comes to marketing)