Maybe Derby County's beginning to go after Division One (7)
I believe the answer is:
classic
'maybe derby' is the definition.
(Epsom Derby is one of the British Classic Races)
'county's beginning to go after division one' is the wordplay.
'beginning to' indicates taking the first letters.
'go after' means one lot of letters go next to another.
'division' becomes 'class' (synonyms).
'one' becomes 'i' (roman numeral).
The initial letter of 'countys' is 'c'.
'class'+'i'='classi'
'c' put after 'classi' is 'CLASSIC'.
(Other definitions for classic that I've seen before include "Having qualities like those of acknowledged art" , "The best of its kind" , "Artistic work of lasting excellence" , "Accepted as excellent" , "Good example of its kind" .)