Arrogant, having been promoted, a matter for regret (6)
I believe the answer is:
uppity
'arrogant' is the definition.
(I've seen this before)
'having been promoted a matter for regret' is the wordplay.
'having been promoted' becomes 'up' (up can mean promoted to another football league).
'a matter for regret' becomes 'pity' (a pity is a shame or regrettable outcome).
'up'+'pity'='UPPITY'
(Other definitions for uppity that I've seen before include "Bumptious" , "Pert; haughty" , "Difficult to control" , "attitude" , "Presumptuously arrogant" .)