Fire-lighting crime of the beheaded vicar? (5)
I believe the answer is:
arson
'fire-lighting crime' is the definition.
(I've seen this before)
'the beheaded vicar?' is the wordplay.
'the beheaded' means to remove the first letter (the head of the word is removed).
'vicar?' becomes 'parson' (both are members of the clergy).
'parson' with its first letter removed is 'ARSON'.
'of' acts as a link.
(Other definitions for arson that I've seen before include "Pyromaniac's crime" , "Torching" , "Fire-raiser's crime" , "Incendiary act" , "matchplay, say?" .)