Body going round worried student pair entering place (9)
I believe the answer is:
satellite
'body going round' is the definition.
(celestial body which orbits another)
'worried student pair entering place' is the wordplay.
'worried' becomes 'ate' (something worrying may eat someone up).
'student' becomes 'l' (as in L-plates for learner drivers).
'pair' indicates the doubling of some letters.
'entering' indicates putting letters inside.
'place' becomes 'site' (synonyms).
'l' duplicated is 'll'.
'ate'+'ll'='atell'
'atell' going inside 'site' is 'SATELLITE'.
(Other definitions for satellite that I've seen before include "Body moving around a planet" , "Moon" , "Country dependent on another" , "Space traveller" , "Lackey" .)