That's a given, and not in question, though the speed restriction does NOT apply outside the STAR and a flight is NOT expected to maintain 270 outside the STAR, unless specifically cleared to do so.
That is not the question, however.
The question regards a flight at the initial fix (KOZAR( listed on the STAR, at FL240, at 300 knots. If the cruise altitude is 300 knots and the airplane arrives at the STAR at 300 knots, the first fix showing a speed restriction is not KOZAR, but EEEZI.
If ATC intends that the flight maintain 280 knots prior to that point, specifically in this case the aircraft arriving at KOZAR in cruise at 300 knots, then ATC will need to include that speed restriction in the clearance, because it's not found on the chart.
A wise pilot will still ask if it's needed.