Play in the headset is usually worn bearings. If you are confident with tools its a simple enough job.
The topcap bolt only eliminatess play during assembly. The headset is actually held in place by the stem. Undo the topcap bolt, then undo the stem pinch bolts with a hex key. Lift the stem and bars clear of the steerer, then pick out the seal, compression ring and any shims or seals, noting the assembly order.
The steerer will now drop out of the head tube.
You will now see the upper bearing race, which may be loose or caged bearings, or a sealed cartridge bearing. If loose bearings, being careful not to lose any, pick them out and clean them with a solvent or gt85. Remove any grease from the bearing cup and inspect for rust or scoring. If its badly pitted or scored you'll need to replace.it. If not, just repack it with clean grease and put the clean bearings back in. Obviously if the bearings are damaaged or.corroded you need to replace them.
Repeat for the lower race.
If the bearings are cartridge type you can check them for wear by using your fingers to turn the inner race surface. If they just feel dry or gritty, you can pick the seal off with a slim pick, flush the old grease.out with the straw of a can of gt85, and then add new grease with a syringe or grease gun before replacing the seal.
To reassemble, pack the crown race.on the fork crown with grease, slide the fork up into the headset being careful not to dislodge the bearings. Push the compression ring, seal and any spacers back in place, and then slide the stem on, leaving it loose for now. Now add the topcap.and bolt, ensuring the cap is.pressing down on either the stem or a spacer, not the steerer.
Tightn the topcap so thatt it just eliminates play, and allows the steerer to turn smoothly in the bearings. Now line up the bars and tighten the stem bolts tight enough to keep everything in place, but not so tight that it won't spin free in a crash.