Dietary regime that's saving me cooking (8)
I believe the answer is:
veganism
'dietary regime' is the definition.
I know nothing about this answer so I cannot judge whether this works.
'saving me cooking' is the wordplay.
'cooking' indicates an anagram (letters cooked up into a new form).
'saving'+'me'='savingme'
'savingme' with letters rearranged gives 'VEGANISM'.
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for veganism that I've seen before include "Life-style choice" , "Dietary practice" .)