Coaster, perhaps, with a piece cut out of the mast (3)
I believe the answer is:
mat
'the mast' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe they are linked in a way I don't understand?
'coaster perhaps with a piece cut' is the wordplay.
'coaster perhaps' becomes 't' (I can't explain this - if you can you should believe this answer much more).
'with' means one lot of letters go next to another.
'a piece' becomes 'man' (man can mean a chess piece).
'cut' means to remove the last letter.
'man' with its last letter removed is 'ma'.
't' after 'ma' is 'MAT'.
'out of' is the link.
Can you help me to learn more?
(Other definitions for mat that I've seen before include "knot" , "Small carpet" , "Tangle" , "carpeting" , "Paint with a dull surface" .)