Incomplete expression of regret involving piece in annual publication (7)
I believe the answer is:
almanac
'annual publication' is the definition.
(I've seen this before)
'incomplete expression of regret involving piece' is the wordplay.
'incomplete' means to remove the last letter.
'expression of regret' becomes 'alack' (archaic word expressing sorrow or regret).
'involving' is an insertion indicator.
'piece' becomes 'man' (man can mean a chess piece).
'alack' with its last letter removed is 'alac'.
'alac' placed around 'man' is 'ALMANAC'.
'in' acts as a link.
(Other definitions for almanac that I've seen before include "Statistical annual" , "Statistical calendar" , "Annual publication containing information in a particular field" , "Annual calendar or handbook" , "issue every year" .)