Gave lessons, reportedly tight (4)
I believe the answer is:
taut
'tight' is the definition.
(I've seen this before)
'gave lessons reportedly' is the wordplay.
'gave lessons' becomes 'taught' (I've seen this before).
'reportedly' indicates a 'sounds like' (homophone) clue.
'taught' is a homophone of 'TAUT'.
(Other definitions for taut that I've seen before include "Without slack" , "seaworthy" , "Stretched tight or disciplined" , "Fully stretched" , "Pulled or drawn tight" .)