Once a person has passed their UK car driving test there is no legal requirement for them to display any sort of 'plate', unless they want too. The green 'new driver' L plate can be a great way to let other drivers know that you have only recently passed your test and might be a little slow off the mark at traffic lights etc, but it is a purely voluntary addition to your car. The green 'P' plate has a similar effect and stands for 'probationer' or 'passed' depending who you believe, but again is something you can 'choose' to fit to your car or simply blend in with the crowd. The choice is yours but my feeling is that a green 'L' could be a good thing if you are using a motorway or dual carriageway for the first time as this will alert following drivers to the fact that you are newly qualified so they should be 'nice' to you.
Good luck with that and safe driving!