There is no exemption.
What you can do is extend the deadlines. Normally, you can exclude the first $250,000 of gain from taxes (or $500,000 if married filing jointly) as long as you owned the home at least 2 years and lived in the home at least 2 of the past 5 years. Meaning basically, you must sell the home in 3 years or less after you move out.
However, if you move out due to military orders or certain other foreign service, you can suspend the time limits for up to 10 years. Meaning, you could sell the house up to 13 years after you moved out and still claim an exclusion of $250,000 or $500,000 of capital gains.
You still pay tax on the rest of the capital gains, and you have to pay depreciation recapture tax on the portion of the capital gains that comes from the depreciation you claimed or could have claimed while the home was a rental.
