noun
Refers to one slice or piece of something, often food. Used as a counter-like noun.
ケーキを一切れください。
Please give me a slice of cake.
パンを一切れ食べた。
I ate a slice of bread.
切れ is a counter for slices or pieces, while 一切れ is a noun meaning one slice/piece.
一片 is more literary and often used for thin, flat pieces or fragments, while 一切れ is everyday for a slice or chunk.
Compound of 一 (ひと, 'one') + 切れ (きれ, 'slice, piece'). The reading ひときれ is a standard combination.