Body going round worried student pair put in place (9)
I believe the answer is:
satellite
'body going round' is the definition.
(celestial body which orbits another)
'worried student pair put in place' is the wordplay.
'worried' becomes 'ate' (something worrying may eat someone up).
'student' becomes 'l' (as in L-plates for learner drivers).
'pair' shows that letters should be duplicated.
'put in' means one lot of letters goes inside another.
'place' becomes 'site' (site is a kind of place).
'l' doubled is 'll'.
'ate'+'ll'='atell'
'atell' going into 'site' is 'SATELLITE'.
(Other definitions for satellite that I've seen before include "Body in orbit around another" , "sidekick" , "dependent community" , "Lackey" , "Space traveller" .)