Support military bands holding African state's flag (5,3,7)
I believe the answer is:
stars and stripes
'flag' is the definition.
(Stars and Stripes is an example)
'support military bands holding african state's' is the wordplay.
I cannot really see how this works, but
'bands' could be 'stripes' ('stripe' can be a synonym of 'band') and 'stripes' is present in the answer.
'african state' could be 'rsa' (Republic of South Africa) and 'rsa' is found in the answer.
'support' could be 'stand' (stand is a kind of support) and 'stand' is located in the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...
(Other definitions for stars and stripes that I've seen before include "American flier" , "indicators of military rank" , "Standard" , "indications of rank" , "The US flag" .)