I am answering because the question's body has this " Do vedas or any scripture.. " in it.
But what about normal animal killing do it have any restrictions?
As you may already expect, normal killing (that is other than when in sacrifices) is never recommended.
Lord Shiva says to Goddess:
Pitridaivatayajneshu vaidha himsA vidhiyate |
himsA kadAchinnoditA priye ||
In Yajnas, meant for Manes and Gods (Pitri Daiva Yajna), animal sacrifices are allowed. But
, O Beloved one, for one's own sake (AtmArtham), killing animals (prAninAm himsA) are never
prescribed in scriptures.
KulArnava Tantram 1.45
In fact, not only animals, even plantations should not be destroyed for our own selfish purposes, which he says in the very next verse:
Swanimittam trinam vyapi chedayenna kadAchana |
For one's own sake one should not even cut a grass.
In the Smritis, atonement measures are prescribed for killing different animals (If you want some such verses, i can provide). And, in them, we can find punishments too, being mentioned for the crimes one commits by destroying plants etc for no good reasons, for one's own selfish use.
Now, the same injunctions can be found in almost every scriptures.
For example, the Manu Smriti says:
5.38. As many hairs as the slain beast has, so often indeed will he who killed it without a (lawful) reason suffer a violent death in
5.52. There is no greater sinner than that (man) who, though not worshipping the gods or the manes, seeks to increase (the bulk of)
his own flesh by the flesh of other (beings).
And, as per it, the lawful reason is when the animal is sacrificed for Gods or Manes (Pitrus).
5.39. Svayambhu (the Self-existent) himself created animals for the sake of sacrifices; sacrifices (have been instituted) for the good of
this whole (world); hence the slaughtering (of beasts) for sacrifices
is not slaughtering (in the ordinary sense of the word).
5.40. Herbs, trees, cattle, birds, and (other) animals that have been destroyed for sacrifices, receive (being reborn) higher existences.
So, normal killing of animals (or even of plants) for purposes other than sacrifices is never recommended in any scriptures. And, this is the conclusion of all scriptures.
Only exception obviously will be the case where the animal is threatening your life, in that case killing it out of self-defense is not a sin, since preserving one's life is the first priority.