Run away, initially finding shelter (4)
I believe the answer is:
flee
'run away' is the definition.
(to flee is to run away)
'initially finding shelter' is the wordplay.
'initially' indicates taking the first letters.
'shelter' becomes 'lee' (as in lee side, the side sheltered from wind).
The initial letter of 'finding' is 'f'.
'f'+'lee'='FLEE'
(Other definitions for flee that I've seen before include "head for the hills" , "Leave" , "Maybe escape" , "Run quickly away" , "Do a runner" .)