adverb
generously; freely; without stint
Used when giving, sharing, or expending effort without holding back; often implies a lack of stinginess or reluctance.
彼は惜しみ無く知識を共有してくれた。
He generously shared his knowledge with me.
惜しみ無くお金を使う。
She spends money freely.
惜しむ is the verb meaning 'to begrudge' or 'to be sparing with'; 惜しみ無く is its adverbial negative form, meaning 'without begrudging'.
From the verb 惜しむ (to begrudge, to be sparing) in its continuative form 惜しみ + 無く (adverbial form of 無い, 'not existing'), literally 'without holding back'.