Should I have any play in my steering stem?

If the play is in the stem you should be able to tighten the stem bolts at the bars and steerer tube to eliminate it. However, it’s more likely your steerer has play within the head tube which can be a little trickier to fix.

Start by loosening the stem cap and the stem bolts at the steerer tube end. Then, roll the front wheel back and forth before grabbing the front brake to nudge the fork/steerer into place. Tighten the stem bolts, then the stem cap. Don’t overtighten as this can affect the steering.

I’ve found it takes a bit of trial and error to get everything seated properly without tightening things too much, so maybe others can weigh in with better tips/instructions.