Has new aspiration to become a ruler (4)
I believe the answer is:
shah
'a ruler' is the definition.
(shah is a kind of ruler)
'has new aspiration' is the wordplay.
'new' indicates an anagram.
'aspiration' becomes 'h' (I've seen this in other clues).
'has' with letters rearranged gives 'sha'.
'sha'+'h'='SHAH'
'to become' is the link.
(Other definitions for shah that I've seen before include "Former Persian ruler" , "Former Iranian ruler" , "Former ruler of Persia" , "Former Iranian leader" , "Persian king" .)