Smile finishing off 500th crossword (4)
I believe the answer is:
grid
'crossword' is the definition.
(a crossword grid)
'smile finishing off 500th' is the wordplay.
'smile' becomes 'grin' (synonyms).
'finishing off' means to remove the last letter.
'500th' becomes 'd' (I can't explain this - if you can you should give a lot more credence to this answer).
'grin' with its last letter removed is 'gri'.
'gri'+'d'='GRID'
Can you help me to learn more?
(Other definitions for grid that I've seen before include "Matrix" , "Line network, pattern" , "a network of squares as in this puzzle" , "Pattern of crossing lines" , "Lattice, mesh" .)