A clan leader fell into disfavor for being a lazy ass. You can also read these books to get an idea
http://www.imperial-library.info/content/code-malacath - An adventurer/sellsword's guide to orc strongholds
http://www.imperial-library.info/content/orsinium-and-orcs - How the orcs won parts of Wayrest
http://www.imperial-library.info/content/true-nature-orcs - A book that shows they're not pig beasts who eat babies.
http://www.imperial-library.info/content/16-accords-madness-v-vii - This orsimer here earned the disfavor of Malacath
Well, there are many reasons why an Orc would be traveling abroad, it wouldn't have to be that he/she was exiled from a stronghold.
But, perhaps the most obvious example I could think of for a reason to be exiled would be that he challenged his father (the chief) to a duel to the death, (as is customary for the title to be passed along) and lost, but ran, as opposed to accepting his fate, or perhaps poisoning or killing an opponent in his sleep, rather than challenging that opponent to an honorable duel.
These too.
Also, males that are too unruly to the current Chief are often sent into exile, or just simply leave for a better shot at life.