Writer’s book supporting part of UK (3)
I believe the answer is:
nib
'writer's' is the definition.
(something which writes)
'book supporting part of uk' is the wordplay.
'book' becomes 'b' (abbreviation for book).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'part of uk' becomes 'NI' (Northern Ireland).
'b' after 'ni' is 'NIB'.
(Other definitions for nib that I've seen before include "Pen-point" , "Writing tip of old pen" , "Pen-tip" , "Part of a fountain pen" , "Writing point of old pen" .)