Pt. Shiv Kumar Sharma, an accomplished Santoor player, originally hails from the State /UT of:

The correct answer is Jammu and Kashmir.

Step-by-Step Explanation:

1. Identity of Pt. Shiv Kumar Sharma: Pandit Shiv Kumar Sharma (1938–2022) was a legendary Indian classical musician and composer who is single-handedly credited with adapting the santoor for Indian classical music.

2. Origin and Instrument History: The santoor is a trapezoid-shaped hammered dulcimer that has its roots as a traditional folk instrument in the valley of Jammu and Kashmir. Shiv Kumar Sharma was born in Jammu to the singer Pandit Uma Dutt Sharma. Under his father's guidance, he began training in both vocal music and tabla, and eventually started learning the santoor to bring the folk instrument onto the classical stage.

3. Conclusion: Therefore, Pt. Shiv Kumar Sharma originally hails from the State/UT of Jammu and Kashmir.