Hmm...
If you want something that is running all the time, you could do it with a service, or with a background thread as Rafa suggests - but before you do either I would have a look at whether your overall design could be improved. Polling the database all the time looking for a new row will mean a lot of unnecessary database traffic...
What's adding the row in the first place? Could we get that code to raise some form of event / invoke an action for us? Depending on the database, are row level triggers available to us? Can we use that to avoid polling?
I don't think you should be actually typing code yet, but rather challenging your current design to see how you might improve it...