I honestly don't know if this is the first major one, there have been a number of border clashes between those two specifically but there have been a number of tensions between various CARs over water rights and control over rail and roadways.
Some details of this specific conflict;
It appears that a border conflict sparked by ethnic tensions erupted into fighting between armed border guard forces from both sides. Each side apparently destroyed a border guards facility of the other side. Overall it kind of looks like Tadjikistan is winning.
Горящая погранзастава. Киргизы заявили, что захватили у таджиков одну погранзаставу. На границе Таджикистана и Киргизии вспыхнули боевые действия. Причиной конфликта стал местный территориальный спор из-за водораздела Головной, который перерос в открытые боевые действия. На данный…
colonelcassad.livejournal.com
Despite the declared cease-fire, sporadic fighting apparently continues. Even Tadjik helicopter (Mi-8 and 24) have been seen.
vk.com
vk.com
Civilians are fleeing and being evacuated in large numbers which unfortunately creates the potential for ethnic cleansing. In at least one case apparently Tadjiks destroyed houses belonging to Kirgiz citizens of Tadjikistan. The second link has footage from one border town in Tadjikistan.
vk.com
vk.com
It also appears that in some cases Tadjik soldiers have taken control over some areas of Kyrgiziya and are raising Tadjik flags.
vk.com
Footage of the conflict.
Сообщают, что в результате боев на таджикско-киргизской границе уничтожена погранзастава Достук Государственной пограничной службы ГКНБ Кыргызстана. Напомню, что боестолкновение между киргизскими и таджикскими военными началось 29 апреля 2021 года на участке водораспределительного…
dambiev.livejournal.com
https://t.me/ChDambiev/7799 https://t.me/ChDambiev/7798 https://t.me/ChDambiev/7797 https://t.me/ChDambiev/7795 https://t.me/ChDambiev/7793 https://t.me/ChDambiev/7794
dambiev.livejournal.com
Artillery moving towards the conflict zone.
vk.com
Allegedly captured Kirgiz soldiers.
vk.com
A presumably Kirgiz BTR-70M destroyed in the fighting.
vk.com
Vice-premier of Kyrgiziya has arrived in Batkenskaya region to de-escalate the conflict.
vk.com