Chaplain might offer tramp religious education (5)
I believe the answer is:
padre
'chaplain' is the definition.
(I know that chaplain can be written as padre)
'tramp religious education' is the wordplay.
'tramp' becomes 'pad' (both can mean to walk around).
'religious education' becomes 'RE' (abbreviation).
'pad'+'re'='PADRE'
'might offer' is the link.
(Other definitions for padre that I've seen before include "Military chaplain" , "Man of god - drape (anag)" , "Cleric" , "Sky pilot (military slang)" , "A military clergyman" .)