Ada, rusty, exercising for twenty-four period (8)
I believe the answer is:
saturday
'twenty-four period' is the definition.
(a 24 hour period)
'ada rusty exercising' is the wordplay.
'exercising' is an anagram indicator.
'ada'+'rusty'='adarusty'
'adarusty' anagrammed gives 'SATURDAY'.
'for' is the link.
(Other definitions for saturday that I've seen before include "Samedi or Sabato or Samstag" , "Its child works hard for living" , "Day named after the sixth planet from the sun" , "24 hours" , "It's Samedi in France" .)