Unfortunately the accent on that audio file is strongly US to my ear.

I googled and got “In North-Eastern English dialect, ‘shy bairns get nowt’ is a well-known idiom that essentially translates to ‘shy children get nothing’. Often used to encourage children (or adults) to speak up and have self-confidence”. The original commenter gidorah has a UK email address. https://www.wordsense.eu/shy_bairns_get_nowt/ looked like a reasonable reference.

My search skills have failed to find it said proper.