On board, the mate puts an end to it (5)
I believe the answer is:
chess
'on board' is the definition.
'chess' can be an answer for 'board' (chess board is a kind of board). I am unsure of the 'on' bit.
'mate puts an end to it' is the wordplay.
'mate puts' becomes 'che' (I can't explain this - if you can you should believe this answer much more).
'an end' suggests removing the centre (I've seen 'ends of' mean this).
'to it' becomes 'sexiness' (I've seen this before).
'sexiness' with its centre taken out is 'ss'.
'che'+'ss'='CHESS'
'the' is the link.
Can you help me to learn more?
(Other definitions for chess that I've seen before include "This is played on board" , "Board game for two players" , "Board game of 13, 16 and 21" , "Game with kings and queens" , "Ancient war game whose name may have derived for the Persian for 'king'" .)