Letter by grand American conservative is worthless (8)
I believe the answer is:
nugatory
'worthless' is the definition.
(similar in meaning)
'letter by grand american conservative' is the wordplay.
'letter' becomes 'nu' (nu is a kind of letter).
'by' says to put letters next to each other.
'grand' becomes 'g' (synonyms).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'conservative' becomes 'tory' (informal term for a Conservative Party member).
'nu'+'g'+'a'+'tory'='NUGATORY'
'is' is the link.
(Other definitions for nugatory that I've seen before include "Insignificant or trivial" , "Futile, of no value" , "Triflingly unimportant" , "Young art (anag) -- worthless" , "to little effect" .)