Egg-laying creature quietly burrowing into ground (8)
I believe the answer is:
terrapin
'egg-laying creature' is the definition.
(terrapins lay eggs)
'quietly burrowing into ground' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'burrowing into' indicates putting letters inside.
'ground' becomes 'terrain' (terrain is land or ground).
'p' placed inside 'terrain' is 'TERRAPIN'.
(Other definitions for terrapin that I've seen before include "Give out" , "Little turtle" , "Water tortoise" , "temporary building" , "Aquatic tortoise" .)