When you donate or upgrade troops you gain experience points that upgrade your king tower to eventually level 13 what happens to experience points after that do they turn to gold like after a card is maxed out?
You do not receive experience points after reaching level 13.
This can be shown in the following picture, where the bar is filled and reads "Max Level". Extra experience points are not generated into any currency.
As of the December 2018 update, ALL XP earned past level 13 will be converted to star points, in addition to Legend trophies! This includes XP past level 13 you may have earned before the update! Star points can be used to upgrade your cards up to Star Level 3, which makes them appear way cooler in a match.
Star Level 1 - cards have gold border, golden 'flash' upon card drop, spells have cool animations
Star levels 2 and 3 - troops/buildings become golden or partially golden/prettier