Odd — square in the centre awfully quiet (10)
I believe the answer is:
uneventful
'quiet' is the definition.
('uneventful' can be similar in meaning to 'quiet')
'odd square in the centre awfully' is the wordplay.
'odd' becomes 'uneven' (I've seen this before**).
'square' becomes 't' (a T-Square is a technical drawing instrument).
'in the centre' means to look at the middle letters.
The middle of 'awfully' is 'ful'.
'uneven'+'t'+'ful'='UNEVENTFUL'
(Other definitions for uneventful that I've seen before include "without much happening" , "dull" , "Quiet" , "without incident" .)