Many enquire for cover (4)
I believe the answer is:
mask
'for cover' is the definition.
(masking is a kind of covering)
'many enquire' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'enquire' becomes 'ask' (synonyms).
'm'+'ask'='MASK'
(Other definitions for mask that I've seen before include "cloak" , "Face covering; disguise" , "Face-cover" , "Camouflage" , "Cover for the face" .)