The Head of the Gelug or "Gelukpas" is the Dalai Lama who is also the head of all the schools of Tibetan Buddhism as well

 

 Begin quote from Google AI and Internet:

Gelug institutions are part of the Gelug tradition, the largest and newest of the four major schools of Tibetan Buddhism, founded by Je Tsongkhapa in the 14th-15th century. Key Gelug institutions include the "great three" monasteries near Lhasa: Ganden Monastery (founder's main seat), Drepung Monastery (largest), and Sera Monastery (known for debates). The tradition emphasizes monastic discipline, rigorous philosophical study of the Buddha's teachings (Sutras and Tantras), and is known for the yellow hats worn by its monks, hence its other name, the "Yellow Hat" sect.
 

Key Characteristics

• Founder:

  Je Tsongkhapa (1357-1419), a renowned Tibetan philosopher and lama. 

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Major Monasteries and Institutions

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  Ganden Monastery:

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Founded by Tsongkhapa in 1409, it served as the main seat of the Gelug school. 

Founded by Jamyang Choje, a disciple of Tsongkhapa, it became the largest Gelug monastery and was the home monastery of the Dalai Lamas. 

Founded by Chöje Shakya Yeshe, it is famous for its monk debates and displays of sand mandalas. 

Tashilhunpo Monastery:

. Located in Shigatse, it was founded by Gyalwa Gendün Drup (the first Dalai Lama) and is the main monastery for the Panchen Lama. 

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Cultural and Political Significance

• The Gelug tradition became the predominant school in Tibet, especially after the enthronement of the Dalai Lamas as spiritual and political rulers in the 17th century. 
  
  

Emphasis:

Strict monastic discipline and a thorough grounding in the doctrines of the sutras before progressing to tantric practices. 

Legacy:

The Gelug tradition traces its roots to the Kadampa tradition founded by Atisha and is sometimes referred to as the "New Kadampa". 

Symbolism:

The "yellow hats" worn by Gelug monks distinguish them and give the tradition its nickname, the "Yellow Sect". 

Drepung Monastery:

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Sera Monastery:

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The Ganden Tripa is the official head of the Gelug school, though the Dalai Lama is its most influential figure.