This fame developing about King is temporary (9)
I believe the answer is:
makeshift
'temporary' is the definition.
('makeshift' can be similar in meaning to 'temporary')
'this fame developing about king' is the wordplay.
'developing' indicates an anagram.
'about' means one lot of letters goes inside another.
'king' becomes 'k'.
'this'+'fame'='thisfame'
'thisfame' with letters rearranged gives 'maeshift'.
'maeshift' going around 'k' is 'MAKESHIFT'.
'is' is the link.
(Other definitions for makeshift that I've seen before include "stopgap" , "Temporary or improvised substitute" , "not meant to last" , "(Acting as) temporary substitute" , "temporary measure" .)