The full question was
At one time no instruments were allowed to play in the temple or the inner court…when were the instruments allowed back in the temple?
I cannot find any record of instruments not being allowed to be played in the temple, except that it was sometimes closed, or in disuse, or even gone (destroyed).
The Law of Moses did not make any rules about the presence or absence of any music as part of the worship associated with the tabernacle (though Moses did teach the people a song to help them remember the law, see Deut 31). But it is evident from a number of passages that music was always central to their worship (Exod 15:1; Judg 5:1), and probably became more widely used, or at least more organized, from the time of David (2 Sam 6:5; 1 Kings 1:40; 1 Chron 16:42; Ezra 3:10; and every one of the Psalms).