A toss-up offers faint prospect (4,3)
I believe the answer is:
pass out
'faint prospect' is the definition.
'pass out' can be an answer for 'faint' (synonyms). I'm not certain of the 'prospect' bit.
'a toss-up' is the wordplay.
'a toss-up' anagrams to 'PASS OUT'.
But, I'm unsure how this is indicated.
'offers' acts as a link.
Can you help me to learn more?
(Other definitions for pass out that I've seen before include "Become unconscious" , "In the army, do so having proved ready" , "Lose consciousness" , "drop" , "keel over" .)