Initially weak old boy showed sign of injury and moved unsteadily (7)
I believe the answer is:
wobbled
'moved unsteadily' is the definition.
('wobble' can be a synonym of 'move unsteadily')
'initially weak old boy showed sign of injury' is the wordplay.
'initially' suggests taking the first letters.
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'showed sign of injury' becomes 'bled'.
The initial letter of 'weak' is 'w'.
'w'+'ob'+'bled'='WOBBLED'
'and' is the link.
(Other definitions for wobbled that I've seen before include "Moved unsteadily" , "Shook precariously" , "Trembled, shook" .)