Job Elizabeth I managed diligently at first (6)
I believe the answer is:
errand
'job' is the definition.
(thesaurus)
'elizabeth i managed diligently at first' is the wordplay.
'elizabeth i' becomes 'ER' (Elizabeth Regina, ie Queen Elizabeth).
'managed' becomes 'ran' (both can mean organised or was in charge of).
'at first' indicates taking the first letters.
The initial letter of 'diligently' is 'd'.
'er'+'ran'+'d'='ERRAND'
(Other definitions for errand that I've seen before include "run one" , "Short commission" , "Commission, task" , "Journey made on someone else's behalf" , "Delivery/collection trip" .)