Try their website as I'm sure the Gunners hold youth tryouts in the close season.
How Do You Get To Try out For The Arsenal Football Youth Academy?
This won't work in all cases, and you'll need luck.
About 10 years ago, my son's local football team played against one of the Arsenal Academy teams (they lost 3-1), but the Arsenal academy people were so impressed with one of the players on my son's team (alas, not my son), that he was invited down to talk to them (at Highbury, in those days). I don't know what happened next. I ran the line that day, so I am able to tell people that I was one of the three officials at an Arsenal match.
About 10 years ago, my son's local football team played against one of the Arsenal Academy teams (they lost 3-1), but the Arsenal academy people were so impressed with one of the players on my son's team (alas, not my son), that he was invited down to talk to them (at Highbury, in those days). I don't know what happened next. I ran the line that day, so I am able to tell people that I was one of the three officials at an Arsenal match.