noun, noun or participle which takes 'suru', transitive verb
setting one's mind at ease; not worrying; feeling free to disregard
Used when one stops worrying about something or decides it is not worth concern. Often appears as 放念する or ご放念ください.
どうぞご放念ください。
Please set your mind at ease.
その件については放念して大丈夫です。
You can stop worrying about that matter.
安心 is a more common word for relief or peace of mind, while 放念 is a somewhat formal expression for consciously letting go of concern.
Compound of 放 (release) and 念 (thought, concern). The exact historical derivation is uncertain, but the kanji transparently suggest 'releasing one's thoughts'.