Come into cool hotel turning weary (7)
I believe the answer is:
inherit
'come into' is the definition.
(synonyms)
'cool hotel turning weary' is the wordplay.
'cool' becomes 'in' ('in' can mean fashionable or cool).
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'turning' shows that the letters should be reversed in order.
'weary' becomes 'tire' (synonyms).
'tire' in reverse letter order is 'erit'.
'in'+'h'+'erit'='INHERIT'
(Other definitions for inherit that I've seen before include "Receive from a deceased parent" , "Receive as heir" , "Receive as bequest from will" , "Succeed as heir" , "Be the recipient of" .)