I forgot a piece of jewelry in Hong Kong, can I get someone to give it to me in the airport while staying in international area?

No, this is not possible. The transfer/airside area of the airport is outside Customs, and it's not possible to bring things in or out of this without going through Customs/security.

The only possibility would be if your friend happens to be boarding a flight at a similar time, so you could meet airside. In more normal times, one option would be for them to buy a fully refundable ticket, use it to enter the airside area and meet you, then refund the ticket and exit. But this seems like an awful lot of hassle, and while I'm not familiar with HKIA's current setup, with COVID restrictions in place I'm not sure it's even possible for outbound passengers to meet transiting passengers or whether they would risk quarantine if they try to exit from airside.

Your best bet is to contact the airport. The simplistic approach, where your friend just shows up at the airport and hands you the item isn't going to work, unless you have a visa that will let you exit the international area or your friend can get access to it.

However it is possible that if you ask nicely and explain then your friend can hand the item to airport customer service and you can collect it in the international area. Or there may be a special pass you can get in exceptional circumstances. I'm not saying it can be done, but it is worth asking. Airports do this occasionally for people who have left items behind during departure.

Depending on the value you might get the item couriered to a business in the international area, but that's a long shot.

As others have said and implied, this would at least look like smuggling. Don't try it.

I'm not familiar with the current COVID regulations at the Hong Kong airport, but why do you have to meet someone in person? If you know where the item is, and you are dealing with an honest person who would give it to you personally, why can't you get them to deliver it to you if you pay the expense of delivery? There may be some hoops to jump through with UK customs and Hong Kong customs, but that way you can avoid any questions and the possible detainment that would cause you to miss your flight to the Philippines.