Upbringing of some Saudi girls is strict (5)
I believe the answer is:
rigid
'strict' is the definition.
('rigid' can be a synonym of 'strict')
'upbringing of some saudi girls' is the wordplay.
'upbringing' is a reversal indicator.
'of some' says the answer is hidden in the clue (I've seen 'some' mean this).
'digir' is hidden within 'saudi girls'.
'digir' reversed gives 'RIGID'.
'is' acts as a link.
(Other definitions for rigid that I've seen before include "stern" , "Frozen" , "Hard" , "Stiff and inflexible" , "Unable to bend" .)