Inept earl admitting baron initially more competent (5)
I believe the answer is:
abler
'more competent' is the definition.
('able' can be similar in meaning to 'competent')
'inept earl admitting baron initially' is the wordplay.
'inept' is an anagram indicator.
'admitting' is an insertion indicator.
'initially' indicates taking the first letters.
The initial letter of 'baron' is 'b'.
'earl' is an anagram of 'aler'.
'aler' placed around 'b' is 'ABLER'.
(Other definitions for abler that I've seen before include "More skilful" , "The better" , "Increasingly smart" , "More accomplished" , "More skilled" .)