Replace the sprocket when the teeth look like shark fins.
Yes, that’s the main sign. A new sprocket has sharp, square-ish teeth. As it wears, the front of each tooth gets a concave curve—hooks inward like a shark’s dorsal fin. That means the chain isn’t seating properly, which causes more wear on both the chain and the bar.
Other signs: the chain gets loose faster than usual, or you feel the drive links skipping under load. If the sprocket is a spur (bare steel), you can see wear just by looking. If it’s a rim sprocket (removable ring), spin the chain by hand and check if the drive links sit deep in the pockets or ride shallow.
Rule of thumb: replace the sprocket with every second or third new chain. Never run a new chain on a worn sprocket—it will wear the chain out fast and can even snap it. If you’re unsure, pop the sprocket cover and compare it to a photo of a new one online. The cost difference is a few bucks; the safety cost is a broken chain at full throttle.