Give up church, ultimately bored and uncooperative (4)
I believe the answer is:
cede
'give up' is the definition.
(I know that give up can be written as cede)
'church ultimately bored and uncooperative' is the wordplay.
'church' becomes 'CE' (abbreviation for Church of England).
'ultimately' indicates one should take the final letters.
'and' is a charade indicator (letters next to each other).
'uncooperative' becomes 'e' (I can't explain this - if you can you should believe this answer much more).
The final letter of 'bored' is 'd'.
'ce'+'d'+'e'='CEDE'
(Other definitions for cede that I've seen before include "Allow" , "Yield formally" , "Surrender or yield" , "Yield or give up to another" , "Surrender or grant" .)