Many have to be cut short (4)
I believe the answer is:
mown
'be cut short' is the definition.
(thesaurus)
'many have' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'have' becomes 'own' (to have something is to own it).
'm'+'own'='MOWN'
'to' acts as a link.
(Other definitions for mown that I've seen before include "(Of grass) cut" , "Cut down with a blade" , "Block of cast metal" .)