This video from India is called Forest Owlet (Athene blewitti) (Heteroglaux blewitti) Call/Song.
From Wildlife Extra:
INDIAN SPECIES REDISCOVERED
India has seen many species disappearing from the wild since the last century.
There have been many which have not been sighted in hundred years; even more.
Some are dead and gone for sure; for some others, hope still flickers among the naturalists and wildlifers.
This optimism is not always misplaced.
There have been a number of species, which have been rediscovered, in the last quarter of the 20th century.
FOREST OWLET (Athene blewitti)
This recently rediscovered species has a tiny, fragmented population known from only four localities.
It is thought to be declining as a result of loss of its deciduous forest habitat.
A crepuscular, diurnal bird, the Forest Owlet lives in dry deciduous forests interspersed with shrubs and grasses and is endemic to Central India.
Until its rediscovery in November 1997, it was known only from seven specimens collected during the 19th century at four localities in two widely separated areas – northern Maharashtra, and southeast Madhya Pradesh/western Orissa.
JERDON’S COURSER (Cursorius bitorquatus)
The Jerdon’s Courser is a rare bird endemic to the Eastern Ghats in Andhra Pradesh and extreme southern Madhya Pradesh.
Historically, it was known from just a few records in the Pennar and Godavari river valleys and was assumed to have been extinct until its rediscovery around Lankamalai in 1986.
Having not been seen since 1895, the bird was rediscovered at Reddipally village in Cuddappah district of Andhra Pradesh.
It has since been sighted at six localities in the vicinity, with all six probably holding birds from a single population. Read more here.
TRAVANCORE EVENING BROWN BUTTERFLY (Parantirrhoea marshalli)
The Travancore Evening Brown, one of the rarest butterflies in the world, was rediscovered in the Periyar Tiger Reserve after a gap of several decades.
It is a brush footed butterfly belonging to the Nymphalidae family.
MALABAR LARGE SPOTTED CIVET (Viverra civettina)
The Malabar Large Spotted Civet was once very common in the coastal districts of Malabar and Travancore in southwest India.
By the late 1960s it was thought to be nearing extinction.
None were seen for a long time until 1987, when it was rediscovered about 60 kilometres east of Calicut in Kerala.
A 1990 survey revealed that isolated populations of the Malabar large spotted civet still survive in less disturbed areas of South Malabar.
ANDAMAN GREEN CALOTES LIZARD (Calotes andamanensis)
This lizard from the Andaman Islands [but see here] was believed to have disappeared forever, till it was rediscovered at the very end of the 20th Century. It is an arboreal and insectivorous reptile.