The writer's holding capital back for part of computer system (6)
I believe the answer is:
memory
'for part of computer system' is the definition.
(as in computer memory)
'the writer's holding capital back' is the wordplay.
'the writer's' becomes 'my' (belonging to the person who set the crossword).
'holding' means one lot of letters goes inside another.
'capital' becomes 'rome' (capital of Italy).
'back' is a reversal indicator.
'rome' back-to-front is 'emor'.
'my' placed around 'emor' is 'MEMORY'.
(Other definitions for memory that I've seen before include "commemoration" , "(Computer) data store" , "See 23" , "The ability to store things in mind, and to recall (6)" , "Mental retention" .)