Start to tuck in old hat label (5)
I believe the answer is:
title
'label' is the definition.
(I've seen this before)
'start to tuck in old hat' is the wordplay.
'start to' suggests taking the first letters.
'in' indicates putting letters inside.
'old hat' becomes 'tile' (tile is an old-fashioned term for hat).
The initial letter of 'tuck' is 't'.
't' put into 'tile' is 'TITLE'.
(Other definitions for title that I've seen before include "Right - name - rank" , "Proprietorship" , "Designation of honour, rank or office" , "Name of book, picture or rank" , "Sign of nobility or name of a work" .)