Go to a nurse about onset of tonsillitis (6)
I believe the answer is:
attend
'go to' is the definition.
('attend' can be a synonym of 'go to')
'a nurse about onset of tonsillitis' is the wordplay.
'nurse' becomes 'tend' (I've seen this before).
'about' means one lot of letters go next to another.
'onset of' indicates taking the first letters.
The initial letter of 'tonsillitis' is 't'.
'tend' after 't' is 'ttend'.
'a'+'ttend'='ATTEND'
(Other definitions for attend that I've seen before include "Be present at, or accompany" , "Be present at (an event)" , "chaperon" , "Be present at, say meeting" , "Completed" .)