Demure being almost nineteen, maybe (4)
I believe the answer is:
prim
'demure' is the definition.
(I've seen this before)
'almost nineteen maybe' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'nineteen maybe' becomes 'prime' (nineteen is a prime number).
'prime' with its last letter taken away is 'PRIM'.
'being' is the link.
(Other definitions for prim that I've seen before include "Prudishly disapproving" , "Straitlaced and proper" , "Schoolmarmish" , "Proper (type of rose?)" , "Prudish, formal" .)