Paper beginning to tackle point in dispute (6)
I believe the answer is:
tissue
'paper' is the definition.
(tissue paper is a kind of paper)
'beginning to tackle point in dispute' is the wordplay.
'beginning to' suggests taking the first letters.
'point in dispute' becomes 'issue' (I've seen this before).
The first letter of 'tackle' is 't'.
't'+'issue'='TISSUE'
(Other definitions for tissue that I've seen before include "cell block?" , "Basic structural element of an animal or plant" , "Paper hanky" , "Jewish religious leader" , "Fine soft paper" .)