Problem gripping Rex in a state (7)
I believe the answer is:
surinam
'state' is the definition.
(Surinam is an example)
'problem gripping rex in a' is the wordplay.
'problem' becomes 'sum' (as in a mathematical problem).
'gripping' means one lot of letters goes inside another (inserted letters are gripped).
'rex' becomes 'R' (abbreviation e.g. GR=George Rex, King George).
'r'+'in'+'a'='rina'
'sum' going around 'rina' is 'SURINAM'.
(Other definitions for surinam that I've seen before include "South American country" , "South American republic, capital Paramaribo" .)