One missing out -- gets nearer, but not number one (5)
I believe the answer is:
loser
'one missing out' is the definition.
(person missing out on a win)
'nearer but not number one' is the wordplay.
'nearer' becomes 'closer' ('close' can be a synonym of 'near').
'but not number one' means to remove the first letter (not the number one letter).
'closer' with its first letter removed is 'LOSER'.
'gets' is the link.
(Other definitions for loser that I've seen before include "One frequently failing" , "Flop" , "Failed competitor" , "Roles for the defeated" , "One who is always a failure" .)