Wiktionary
vb. (context idiomatic English) To relax or feel secure about something.
Wikipedia
"Breathe Easy" is a song written by Lars Halvor Jensen, Martin Michael Larsson and Lee Ryan and released by the British boyband Blue. The song was included on their third studio album, Guilty. It was released as a single on 22 March 2004 in the United Kingdom. An Italian version of the song, entitled "A Chi Mi Dice", was released as a single in Italy, the lyric was written by Tiziano Ferro. In December 2012, Daniel Evans, A finalist on The X Factor published an acoustic piano driven ballad version on his YouTube channel. This was subsequently released on iTunes as part of "The Covers Collection EP Vol.2"
Usage examples of "breathe easy".
It should be all right to leave him alone, but she wouldn't breathe easy until she was back home and could see that for herself.
Only when the powder had been washed down his throat could Kylock breathe easy again.