Day of rest that occasionally pop group's taken up (7)
I believe the answer is:
sabbath
'day of rest' is the definition.
(Sabbath is an example)
'that occasionally pop group's taken up' is the wordplay.
'occasionally' means one should take alternating letters (letters taken at regular intervals or occasions).
'pop group's' becomes 'ABBA's' (Swedish pop band).
'taken up' says the letters should be written backwards.
The alternating letters of 'that' are 'ht'.
'ht'+'abbas'='htabbas'
'htabbas' backwards is 'SABBATH'.
(Other definitions for sabbath that I've seen before include "Sacred day of the week" , "Day of rest and worship" , "Hebrew word for day of rest" , "Religious day of rest for Jews and Christians" , "Period of rest" .)