Earnestly desire praise perhaps (6)
I believe the answer is:
aspire
'earnestly desire' is the definition.
(I've seen this before)
'praise perhaps' is the wordplay.
'perhaps' is an anagram indicator.
'praise' is an anagram of 'ASPIRE'.
(Other definitions for aspire that I've seen before include "Long" , "Have lofty aims" , "Have ambitions (to achieve something)" , "Have hopes (to achieve something)" , "Have an ambitious plan or a lofty goal" .)