Tutored in speech as not relaxed (4)
I believe the answer is:
taut
'not relaxed' is the definition.
(I've seen this in another clue)
'tutored in speech' is the wordplay.
'tutored' becomes 'taught' (synonyms).
'in speech' indicates a 'sounds like' (homophone) clue.
'taught' is a homophone of 'TAUT'.
'as' acts as a link.
(Other definitions for taut that I've seen before include "On the slope" , "Held in tension" , "Stretched tight or disciplined" , "Pulled or drawn tight" , "Fully stretched" .)