Lawful to go after former president, that's clear (8)
I believe the answer is:
explicit
'clear' is the definition.
(I've seen this before)
'lawful to go after former president' is the wordplay.
'lawful' becomes 'licit' (synonyms).
'to go after' says to put letters next to each other.
'former' becomes 'ex' (prefix meaning former or onetime).
'president' becomes 'p' (common abbreviation eg in VP).
'ex'+'p'='exp'
'licit' put after 'exp' is 'EXPLICIT'.
'that's' acts as a link.
(Other definitions for explicit that I've seen before include "Distinctly stated" , "Spelt out, clear" , "Stating something in exact terms" , "Clearly observable" , "Stated or shown directly, not ambiguous" .)