TV award? One's used to prize, though not first (4)
I believe the answer is:
emmy
'tv award?' is the definition.
(I've seen this before)
'one's used to prize though not first' is the wordplay.
I cannot quite understand how this works, but
'one's' could be 'my' (both can mean belonging to the person writing) and 'my' is found within the answer.
The remaining letters 'em' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for emmy that I've seen before include "Television equivalent of Hollywood's Oscar" , "Uncle Sam's award" , "TV Oscar" , "British television award" , "prize for set work" .)