In Newcastle perhaps persist, regularly making demand (9)
I believe the answer is:
necessity
'demand' is the definition.
(necessity is a kind of demand)
'in newcastle perhaps persist regularly' is the wordplay.
'in' means one lot of letters goes inside another.
'newcastle' becomes 'ne' (I've seen this in other clues).
'perhaps' becomes 'city' (I can't explain this - if you can you should give a lot more credence to this answer).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternate letters of 'persist' are 'ess'.
'ne'+'city'='necity'
'necity' placed around 'ess' is 'NECESSITY'.
'making' acts as a link.
Can you help me to learn more?
(Other definitions for necessity that I've seen before include "Something essential or indispensable" , "Fundamental" , "Great need" , "It's said to be the mother of invention" , "Need, exigency" .)