First-class bishop, single chap, backing state (7)
I believe the answer is:
namibia
'state' is the definition.
(Namibia is an example)
'first-class bishop single chap backing' is the wordplay.
'first class' becomes 'ai' (Am - top quality).
'bishop' becomes 'b' (abbreviation used in chess).
'single' becomes 'i' (one).
'chap' becomes 'man' (I've seen this before**).
'backing' is a reversal indicator.
'ai'+'b'+'i'+'man'='aibiman'
'aibiman' reversed gives 'NAMIBIA'.
(Other definitions for namibia that I've seen before include "African republuc" , "SW African state" , "Southwest African country" , "South West Africa" , "African country, capital Windhoek" .)