Lacking strength, reportedly, for seven days (4)
I believe the answer is:
week
'seven days' is the definition.
(I've seen this before)
'lacking strength reportedly' is the wordplay.
'lacking strength' becomes 'weak' (I've seen this before).
'reportedly' shows a homophone (sound like).
'weak' is a homophone of 'WEEK'.
'for' acts as a link.
(Other definitions for week that I've seen before include "Seven days" , "Part of the year" , "Calendar period" , "Seven day period" , "Period of time; sounds like feeble" .)