Doctor Sara with duty for twenty-four period (8)
I believe the answer is:
saturday
'twenty-four period' is the definition.
(a 24 hour period)
'doctor sara with duty' is the wordplay.
'doctor' indicates anagramming the letters.
'with' means one lot of letters go next to another.
'sara'+'duty'='saraduty'
'saraduty' anagrammed gives 'SATURDAY'.
'for' is the link.
(Other definitions for saturday that I've seen before include "Samedi or Sabato or Samstag" , "24 hours" , "Day named after the sixth planet from the sun" , "when many are out of work" , "Jewish Sabbath" .)