Burning egg, not wanting bagel (6)
I believe the answer is:
urgent
'burning' is the definition.
(I've seen this before)
'egg not wanting bagel' is the wordplay.
'egg' becomes 'urge' (I've seen this in another clue).
'wanting' is a deletion indicator (to want something can mean to lack it or need it).
'bagel' becomes 'O' (bagel can mean a score of zero in tennis).
'not' with 'o' taken out is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Needing immediate action" , "Requiring speedy action" , "Pressing, burning" , "Needing immediate attention, don't delay" , "Earnest, insistent" .)