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Fault slip rates are critical to quantify continental deformation. Those along the Karakax fault (northwestern Altyn Tagh Fault: ATF) have been debated, even though it is one of Tibet's most outstanding active faults. At Taersa, using LiDAR measurements of terrace and fan riser offsets (∼6 to ∼500 m) and 10Be/26Al dating of alluvial surfaces (<210 ka), we obtain a late Quaternary slip rate of ∼2.5 ± 0.5 mm/yr. This doubles the ∼2.6 ± 0.5 mm/yr rate time span found to the east and west. We interpret the ∼150 km‐long, free‐faced rupture along the fault to be that of the M ∼ 7.6 event felt in Hotan in 1882. Characteristic slip (∼6 m) during four large earthquakes since ∼10 ka implies a ∼2500 ± 500 years return time. A ∼3 mm/yr rate is consistent with the ∼80 km offset of the Karakax river since uplift of the West Kunlun range and sediment deposition in the Tarim foreland accelerated, ∼24 Ma ago. The faster slip rate (∼10.5 mm/yr) on the central ATF matches the sum of those along the reactivated West Tibetan terrane boundaries (Karakax and Longmu‐Gozha Co faults) at the Uzatagh triple junction (∼36°N, 83°E). The abrupt termination and altitude drop of the Karakorum range where the Longmu Co and Karakorum faults meet (Angmong junction), also reflect triple junction kinematics. Such localized changes account for the rise of the Karakorum and West Kunlun ranges and support lithospheric block tectonics rather than diffusely distributed deformation. Plain Language Summary: How the Tibetan plateau rose to ∼4500 m and deforms today remain outstanding questions. Tibet's northern edge follows the ∼2000 km‐long ATF, whose westernmost branch is the Karakax fault. Despite the spectacular escarpments and offsets observed along that fault, its slip rate, critical to quantify continental deformation, has remained controversial. Here, we corroborate that, for the last ∼210,000 years, that rate has been ∼2.5 ± 0.5 mm/yr, based on high‐resolution topography and dating of left‐laterally offset fluvial surfaces. The ∼80 km offset of the Karakax river implies that this rate may have remained constant since the rise of the Kunlun range above the Tarim basin started ∼24 Ma ago. The sharp fault trace reflects the exceptional preservation, since ∼10,000 years ago, of four M ∼ 7.6 earthquake ruptures (the last in 1882), each with ∼6 m of slip (∼2500 years return time). Fault slip rates, GPS vectors and mountain altitudes across western Tibet reflect block motions and triple junction kinematics rather than continuum deformation. Specifically, localized velocity changes appear to account for the rise of the West Kunlun and Karakorum ranges. Our results bridge the gaps between present and long‐term geological history, and broad‐scale geodesy and local field evidence. Key Points: The ∼400 km‐long, left‐lateral Karakax fault (western Altyn Tagh fault) slip rate has been ∼2.5 ± 0.5 mm/yr for ∼210 kaFour M ∼ 7.6 earthquakes (150 km rupture length; 2.5 ka return time) have offset Holocene terraces (6, 12, 18, and 24 m characteristic slip)Block tectonics and triple junction kinematics account for 24 Ma deformation of west Tibet and rise of ≥8000 m‐high Karakorum range [ABSTRACT FROM AUTHOR]