The name of Śarabha is first mentioned in the Rig Veda, in the hymn to Indra and Vāyu, he is mentioned as a relative of ṛṣi (शरभाय ऋषि बन्धवे śarabhāya ṛṣi bandhave):
विश्वेत्ता ते सवनेषु प्रवाच्या या चकर्थ मघवन्निन्द्र सुन्वते ।
पारावतं यत्पुरुसम्भृतं वस्वपावृणोः शरभाय ऋषिबन्धवे ॥६॥
viśvettā te savaneṣu pravācyā yā cakartha maghavannindra sunvate ।
pārāvataṃ yatpurusambhṛtaṃ vasvapāvṛṇoḥ śarabhāya ṛṣibandhave ॥ 6 ॥
Oh, Meghavan (the name of Indra, who was crowned on Mount Mekhvan)! All your actions, which grant the well-being to Pārāvana and gathered in large numbers for Śarabha, who is a relative of ṛṣi, are worthy of praise at performing sacrifices.
Besides the mention, also, in the Atharva Veda, an interesting reference of Śarabha is found in Śatapatha-brahmana, where he is mentioned as kimpuruṣa (a half-human, a half-animal):
स यं पुरुषमालभन्त । स किम्पुरुषोऽभवद्यावश्वं च गां च तौ गौरश्च गवयश्चाभवतां यमविमालभन्त स उष्ट्रोऽभवद्यमजमालभन्त स शरभोऽभवत्तस्मादेतेषां पशूनां नाशितव्यमपक्रान्तमेधा हैते पशवः – १.२.३.
sa yaṃ puruṣamālabhanta। sa kimpuruṣo’bhavadyāvaśvaṃ ca gāṃ ca tau gauraśca gavayaścābhavatāṃ yamavimālabhanta sa uṣṭro’bhavadyamajamālabhanta sa śarabho’bhavattasmādeteṣāṃ paśūnāṃ nāśitavyamapakrāntamedhā haite paśavaḥ – 1.2.3.
He is the person whom they offered as a sacrifice, he became kimpuruṣa; the horse and the bull, which they sacrificed, became a female and a male buffalo, and the sheep that was killed became a camel, the killed goat became Śarabha. These animals cannot be eaten, because they are devoid of sacrificial essence. 1.2.3.
Later, Śarabha, also known as Śalabha, is also found in the following Purāṇas (Śriīmadbhāgavata, Matsya, Skanda, Harivamśa, Śiva and Padma Purāṇas), as well as in the Mahābhārata (Vana Parva, Śanti Parva, Adi Parva, Udyoga Parva, Droṇa Parva), in the Rāmāyaṇa (in Yuddhakanda) and also in various forms in the most diverse Tantras. Often he is described as a Deity having four paws, which symbolise the eight forms of Śiva, his thighs symbolise the vyādhi (illnesses) and mṛityu (death) that he controls. His stomach is Vadavagni Bhairava, Bālātripurasundari is in his heart, in the two wings there are the Goddesses –Śulini Durgā and Pratyaṅgirā, in the throat there is Mahakala Bhairava, in his eyes – the sun, the moon and fire, in his claws there are vajras of Indra. He also has the face of a lion.
Basically, Śarabha is known to many upāsakas as a form of Bhairava, who prevented the contamination with the blood, that Narasiṃha had drunk, killing the demon Hiraṇyakaśipu. The story is that Hiraṇyakaśipu performed austerities in order to gain the strength not to be killed either on earth or in the air, in the room or on the street, by animals or by men. Then Viṣṇu appeared in the guise of a half-lion, half-man. It happened on the steps of a palace (neither in the house nor on the street), he raised Hiraṇyakaśipu and killed him on his own knee (neither on earth nor in the air). However, after drinking the blood of Hiraṇyakaśipu, Narasiṃha began to fall under his demonic influence. For that purpose Śiva took the form of Śarabheśvara, raised Narasiṃha above the earth and “dropped” him so that he spewed all the blood of Hiraṇyakaśipu out of himself. Sometimes Śarabheśvara is called Aśu Garuḍa because he has the ability to fly. In that sense, Śarabha symbolises the strength of a large number of living beings. A modern example might be given: when new types of weapons are being developed, with more sophisticated program control and functional capabilities. In fact, Śarabha is a kind of Deity with Narasiṃha‘s “improved” abilities, more advanced to combat demons, with more flexible methods of warfare.
His name Śalabha, which translates as “grasshopper”, means that the insect is capable of making jumps that resemble a flight, although in general it is on the ground. In honour of him, there is a well-known śalabhāsana in yoga, which is quite powerful; Śalabha or Śarabha is a symbol of strength, he is full of Śakti (energy). Narayanasvami gives a yogic interpretation of the image of Śarabha in his text Tantrika Mahākāvya, for example, that his eight paws mean aṣṭāṅga-yoga, four of them look upwards (antaraṅga-yoga) and four – down (bahiraṅga–yoga). However, it seems to me, Śarabha can rather be associated with different kinds of living beings and their forces, as many yoga texts say, there are as many yogic āsanas as living beings. Mastering of āsanas could mean even more than the ability to take different positions of the body, but also probably the awareness of the various vibrational characteristics that fill the entire universe, to realise the main ability – to become a siddha-puruṣa and get out of the influence of saṃsāra and māyā. Śarabha is a Deity who removes a magical enchantment, takes the practitioner out of bewitchment by an illusory force. Therefore, he is able to grant spiritual liberation. However, the Deity includes a conglomerate of very different energies, so he is capable of giving a strong transformation, thus sādhaka should have strong self-control and be mature. Tremendous devotion to a real Guru (realised Siddha), who has realised this Deity and its mantras in himself and can transmit it in its full state to his own śiśya is a necessary part. Otherwise, mantras of Śarabha, Pratyaṅgirā, and others can greatly damage the experimenter with such mantras and sādhanas. In connection with that, I won’t make any technical information on the practice of such Deities publicly available.
Returning to the theme of yoga, a very interesting description of śarabhāsana is found in the Agama-rahasya-tantra, where many āsanas are described by the same names as in the texts of haṭha-yoga (as understood by many now). However, these āsanas are often described as mats made of different materials, on which one must sit and chant a mantra a certain number of times, which leads to different siddhis. For example, mayūrāsana, siṁhāsana, kukkuṭāsana, etc. are different materials from animal skin. But speaking of śarabhāsana, confusion may arise, because there is no such “animal” in the real nature. Respectively, the conclusion is: āsanas also mean the image itself, which carries this or that kind of force.