Bovine emission thought at first to be irrelevant (4)
I believe the answer is:
moot
'be irrelevant' is the definition.
(I've seen this in another clue)
'bovine emission thought at first' is the wordplay.
'bovine emission' becomes 'moo' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'at first' indicates taking the first letters.
The initial letter of 'thought' is 't'.
'moo'+'t'='MOOT'
'to' is the link.
Can you help me to learn more?
(Other definitions for moot that I've seen before include "Such a point is arguable" , "Open to question" , "Open to argument or debate" , "Propose for discussion" , "Controversial" .)