This may not be exactly what you're looking for, but the thirteenth-century Republic of Genoa (Italy) would employ a foreign noble as their ruler (the podesta) in an attempt to quell conflict between two clan-based parties - the Menacianos and Camadimos (think Shakepeare's Capulets and Montagues) - which undermined their economic development and caused various problems.

The idea was to design the position to maximize neutrality in ruling. The podesta would be serve for a year, and was supported by a staff which he brought with him. He was paid handsomely and given a bonus if there was no civil war when he left office. He was prohibited from socializing or dealing with the Genoese - buying property, getting married, or participating in other transactions on his own behalf. After leaving office, he wouldn't be allowed to return for several years.

This lasted for about 150 years. A very unique setup.

Source: Hechter, Michael. Alien Rule. Cambridge University Press (2013)