Peer around state north of India's capital (7)
I believe the answer is:
nairobi
'capital' is the definition.
(capital of Kenya)
'peer around state north of india's' is the wordplay.
'peer' becomes 'nob' (nob can mean an aristocrat).
'around' indicates putting letters inside.
'state' becomes 'air' (as in airing or stating an opinion).
'north of' means one lot of letters go next to another (in a down clue, some letters go above others).
'india' becomes 'i' (phonetic alphabet: alpha, bravo, charlie etc.).
'nob' placed around 'air' is 'nairob'.
'nairob'+'i'='NAIROBI'
(Other definitions for nairobi that I've seen before include "City of Kenya" , "Foreign capital" , "Robinia strangely found in Kenya" , "The capital of Kenya (7)" , "African city" .)