Will the trouble code still appear after you fix the problem

Usually when you get your vehicle serviced, the technician will reset the computer of your car. I read that different makes of vehicles have different ways of resetting the computer. Such as stepping on the gas pedal three times while the engine is off. Ask around to see how your own make is reset.

The same reader that is used to pull the codes is also able to clear the codes. To answer your question, yes, the code remains, to some extent. Most manufacturers program in an automatic reset that triggers after a failure has occured and a predetermined number of "key-ons" has occured, but the number is always different. For example, a given sensor shows a fault, and a code is generated by the PCM. Suppose that no repair is made, and the failure was a transient thing, and does not occur again. After a predetermined number of times of turning the key on, say 50, with no failures being detected, the code goes away. This is a "usually, but not always" thing.

Best plan have the codes cleared by a reader so that if they exist later, you know for certain that the code was generated again rather than "still existing".

Best of luck to you.