Limp through small deficiency (5)
I believe the answer is:
slack
'limp' is the definition.
(thesaurus)
'small deficiency' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'deficiency' becomes 'lack' (synonyms).
's'+'lack'='SLACK'
'through' is the link.
(Other definitions for slack that I've seen before include "Flaccid" , "Limp - negligent" , "Lazy and careless" , "Not taut" , "coal dust" .)