Lobsang Dhondup, who was sentenced with him, was executed last year.
Tenzin Deleg Rinpoche has appealed against his conviction, and rights groups have dismissed the charges against him as groundless.
Now that the suspension to his death sentence has run out, some rights groups have expressed concern the sentence could be carried out, although suspended death sentences are usually followed by life imprisonment in China.
The Dalai Lama called for the death sentence to be lifted.
"I hope, as in the past in some cases, the Chinese government and concerned officials will reconsider the death sentence," the Dalai Lama told reporters in the southern Indian city of Bangalore.
But a spokeswoman for Beijing's foreign ministry called Tenzin Deleg Rinpoche a "terrrorist".
"In any country for these criminals that jeopardise national security and engage in terrorist bombings, they will meet punishment according to law," said Zhang Qiyue.
Tenzin Deleg Rinpoche and Lobsang Dhondup were found guilty of carrying out two attacks in the region of Ganzi, near Tibet's eastern border, and another in April 2002 on Sichuan province's capital, Chengdu, which left one person dead.
The area in which the attacks allegedly took place has a large ethnic Tibetan population and a history of independence activity.
Western Sichuan was originally known as Cham and was historically part of Tibet.
After the Communists came to power in China in 1949, they amalgamated Cham into Sichuan province.
The following year, China's People's Liberation Army invaded and occupied the rest of Tibet.
The Dalai Lama fled into exile in 1959.
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