If you don't want the reel to spin when you start the engine, you need to disengage the clutch in the engine shaft, between the engine and the chain case. If the clutch drives when you have the lever in the disengaged position, the clutch is misbehaving, but this is not difficult to fix. You have to see whether the two halves of the clutch separate, compressing the spring, or not. If the spring does not become compressed, there is a problem in the clutch external mechanism.

There is nothing wrong with taking it to the mower shop, but there is more satisfaction in at least finding out what is wrong, before you do it.