Heading back east late, he would dry out (9)
I believe the answer is:
dehydrate
'dry out' is the definition.
(dehydrating is a kind of drying out)
'heading back east late he would' is the wordplay.
'heading back' says the letters should be written backwards.
'east' becomes 'e' (abbreviation).
'late' becomes 'tardy' (synonyms).
'would' becomes 'd' (as in 'we'd' - 'we would').
'e'+'tardy'+'he'+'d'='etardyhed'
'etardyhed' in reverse letter order is 'DEHYDRATE'.
(Other definitions for dehydrate that I've seen before include "Remove moisture from, make dry" , "Deprive of water" , "Lose a lot of water" , "Preserve by removing all liquid from" , "Remove water from" .)