Oddly Star Trek: Discovery 's leading character is fed up (5)
I believe the answer is:
sated
'fed up' is the definition.
(sated can mean completely fed)
'oddly star trek discovery 's leading character' is the wordplay.
'oddly star trek discovery ' becomes 'sate' (I can't explain this - if you can you should give a lot more credence to this answer).
'leading' says to put letters next to each other.
'character' becomes 'd'.
'sate'+'d'='SATED'
'is' is the link.
(Other definitions for sated that I've seen before include "Fully satisfied" , "Stuffed with food, too full" , "with no empty spaces?" , "fully filled" , "Stuffed, having had a surfeit" .)