Live without sex? That's something to chew on! (4)
I believe the answer is:
bite
'that's something to chew on' is the definition.
(as in a bite of food)
'live without sex?' is the wordplay.
'live' becomes 'be' (synonyms).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'sex?' becomes 'it' (a common euphemism).
'be' going around 'it' is 'BITE'.
(Other definitions for bite that I've seen before include "(Of fish) take the bait" , "Clamp down teeth" , "Light meal" , "Nip; nibble" , "Take bait; sting" .)