Quiet spot to grab shelter (6)
I believe the answer is:
sleepy
'quiet' is the definition.
(I've seen this before)
'spot to grab shelter' is the wordplay.
'spot' becomes 'spy' (synonyms).
'to grab' is an insertion indicator.
'shelter' becomes 'lee' (as in lee side, the side sheltered from wind).
'spy' enclosing 'lee' is 'SLEEPY'.
(Other definitions for sleepy that I've seen before include "Ready to nod off" , "Quiet" , "Drowsy; indolent" , "Dozy" , "Doc's nodding pal" .)