Did you water is copiously when it was younger? Has it had any blossom this year? If both answers are "yes", it certainly should have fruited by now.

The Greengages in our hedgerow produce fruit about once every 5 years. They seem to flower at a bee free time. Not sure if they are cross pollinated by Damson or other plums which flower at the same time and do produce fruit.

Yea, the important question is, has it blossomed yet? Greengages usually flower quite early in the year

If it hasn't flowered, is it getting at least 6 hours of direct sun a day? Too much shade will prevent bloom. Too much high nitrogen food will delay bloom for a few years, while the tree grows as far as it can. Too much pruning can also prevent bloom, though you would practically have to pollard it for that to happen.