Claim Yorkshire town lacks aspiration (8)
I believe the answer is:
arrogate
'claim' is the definition.
(arrogate means to claim or take)
'yorkshire town lacks aspiration' is the wordplay.
'yorkshire town' becomes 'harrogate' (I've seen this before).
'lacks' is a deletion indicator.
'aspiration' becomes 'h' (speech sound from a puff of breath).
'harrogate' with 'h' taken out is 'ARROGATE'.
(Other definitions for arrogate that I've seen before include "Ascribe or claim as one's own" , "Appropriate" , "Falsely claim" , "Claim for oneself without justification" , "Assume" .)