Clue: Natural lining material wrapped round end of the contents of basket (5)
Answer: MOSES
Explanation: Definition: contents of basket
~~E (last letter of the middle letters of bASKEt – a rather unusual construction) in MOSS~~ *Ignore that rubbish: it's "end of thE" in MOSS, and the infant Moses was found by hidden in an "ark of bulrushes", i.e. a basket, where he was found by Pharaoh's daughter