Papers regularly give gift (7)
I believe the answer is:
pressie
'gift' is the definition.
(short for 'present')
'papers regularly give' is the wordplay.
'papers' becomes 'press' (I've seen this before**).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'give' are 'ie'.
'press'+'ie'='PRESSIE'
(Other definitions for pressie that I've seen before include "Something freely given" , "Informally, offering" , "Gift (colloq.)" .)