Boss almost making a tactless remark (5)
I believe the answer is:
gaffe
'a tactless remark' is the definition.
(I've seen this before)
'boss almost' is the wordplay.
'boss' becomes 'gaffer' ('gaffer' can be a synonym of 'boss').
'almost' means to remove the last letter (most of the word but not all of it).
'gaffer' with its final letter taken off is 'GAFFE'.
'making' acts as a link.
(Other definitions for gaffe that I've seen before include "A blunder, faux pas" , "embarrassing error" , "Brick (that's dropped)" , "bad mistake" , "Tactless remark" .)