Obligations best dealt with by the deputy-head (5)
I believe the answer is:
debts
'obligations' is the definition.
('debt' can be a synonym of 'obligation')
'best dealt with by the deputy-head' is the wordplay.
'dealt with' indicates an anagram.
'by' means one lot of letters go next to another.
'the deputy-head' becomes 'd' (head letter of 'deputy-').
'best' anagrammed gives 'ebts'.
'ebts' after 'd' is 'DEBTS'.
(Other definitions for debts that I've seen before include "Liabilities" , "Financial obligations" , "Moneys owed" , "Outstanding sums" , "They're owed" .)