Parent cut up about teenager, primarily (5)
I believe the answer is:
pater
'parent' is the definition.
(pater is a kind of parent)
'cut up about teenager primarily' is the wordplay.
'cut' becomes 'reap' (I've seen this before).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'about' indicates putting letters inside.
'primarily' indicates taking the first letters.
The initial letter of 'teenager' is 't'.
'reap' reversed gives 'paer'.
'paer' placed around 't' is 'PATER'.
(Other definitions for pater that I've seen before include "Our Father - . . . . . Noster" , "Taper away like father" , "A posh father, from Latin" , "Walter --, English essayist; father" , "Dad (Latin)" .)