Krdytkyu

Is Law of Karma something which acts on its own? Or are there some sentient beings which implement it? Is it something which acts automatically without involvement of God?

For eg., if a person gets a slight injury. It could be due to some past karma of his. But who is the agent which decides that this injury needs to be afflicted? Is it God, or some other deity?

It does not act on its own. There are no sentient beings that implement it. Iswara, the sentient Being, does implement it. Brahma Sutras 3.2.38 says (available here - https://www.wisdomlib.org/hinduism/book/brahma-sutras Swami Vireswarananda translator):

Brahma-Sutra 3.2.38: Sanskrit text and English translation.

फलमतः, उपपत्तेः ॥ ३८ ॥

phalamataḥ, upapatteḥ || 38 ||

phalam—Fruits of actions; ataḥ—from Him; upapatteḥ—for that is reasonable.

38. From Him (the Lord) are the fruits of actions ; for that is reasonable.

Having described the nature of Brahman, the author proceeds now to discuss the view of the Mimamsakas, who say that Karma (work) and not Īswara gives the fruits of one’s actions. According to them(?) it is useless to set up an Iswara for this purpose, since Karma itself can give that result at a future time.

This Sutra refutes it and says that from Iswara alone come the fruits cf one’s work. Karma is insentient and short-lived, and cannot therefore be expected to bestow the fruits of actions at a future time according to one’s deserts. We do not see any insentient thing bestow fruits on those who worship it. Therefore it is only from the Lord, who is worshipped through actions, that their results proceed.

and verse 39:

Brahma-Sutra 3.2.39: Sanskrit text and English translation.

श्रुतत्वाच्च ॥ ३९ ॥

śrutatvācca || 39 ||

śrutatvāt—Because the scripture so teaches; ca—and.

39. And because the scripture so teaches.

The scripture declares that the fruits of actions come from the Lord. “That great, birthless Self is the eater of food and the giver of wealth (the fruit of one’s work)” (Brih. 4. 4. 24).

and verse 41:

Brahma-Sutra 3.2.41: Sanskrit text and English translation.

पूर्वं तु बादरायणः, हेतुव्यपदेशात् ॥ ४१ ॥

pūrvaṃ tu bādarāyaṇaḥ, hetuvyapadeśāt || 41 ||

pūrvam—The former (i.e. the Lord); tu—but; bādarāyaṇaḥ—Badarayana; hetu-vyapadeśāt—on account of His being declared to be the cause (of the actions even).

41. But Badarayana (thinks) the former (the Lord, as the bestower of the fruits of actions) on account of His being declared to be the cause (of the actions even).

‘But’ refutes the view of Sutra 40. Both Karma and Apurva are insentient, and as such incapable of producing results without the intervention of an intelligent principle. For such a phenomenon is not experienced in the world. No one gets anything by worshipping stocks and stones. So the fruits of actions come only from the Lord, and this is all the more established, as the Lord Himself causes people to act one way or the other; and since the Jiva acts as directed by Him, He Himself is the bestower of the fruits of his actions according to his deserts. “He makes him whom He wishes to lead up from these worlds do a good deed” etc. (Kau. 3. 8); “Whichever divine form a devotee wishes to worship . . . and obtains from it the results he desires, as ordained by Me” (Gita 7. 21-22). Since the Lord has regard for the merit and demerit of the souls, the objection that a uniform cause is incapable of producing various effects does not stand.

Iswara is the only giver of the fruits of your actions.