Annually repeated circuit round the centre of Paris was gripping (5)
I believe the answer is:
orbit
'annually repeated circuit' is the definition.
(orbit of the sun)
'round the centre of paris was gripping' is the wordplay.
'round' becomes 'o' (round can mean a round object).
'the centre of' indicates the central letters.
'was gripping' becomes 'bit' (bite can mean to grip).
The middle of 'paris' is 'r'.
'o'+'r'+'bit'='ORBIT'
(Other definitions for orbit that I've seen before include "Sun's circulation" , "Circling path" , "revolutionary course" , "Track of satellite" , "Circle in space" .)