I was first out, but refused to admit it (4)
I believe the answer is:
lied
'refused to admit it' is the definition.
(I've seen this before)
'i was first out' is the wordplay.
'was first' becomes 'led' (to lead is to go first).
'out' is an insertion indicator.
'i' put into 'led' is 'LIED'.
'but' acts as a link.
(Other definitions for lied that I've seen before include "Art song - told porkies" , "Idle (anag.)" , "conveyed a false impression" , "Romantic song told a story" , "Stated falsely" .)