Illegally obtain dossier about horse (7)
I believe the answer is:
finagle
'illegally obtain' is the definition.
'dossier about horse' is the wordplay.
'dossier' becomes 'file' (I've seen this before).
'about' indicates putting letters inside.
'horse' becomes 'nag' (nag is a kind of horse).
'file' going around 'nag' is 'FINAGLE'.
(Other definitions for finagle that I've seen before include "Swindle" , "Dishonestly obtain" , "cheat" .)