He brings up English cases to run through (8)
I believe the answer is:
rehearse
'run through' is the definition.
(I've seen this before)
'he brings up english cases' is the wordplay.
'brings up' becomes 'rears' (rearing is a kind of bringing up**).
'english' becomes 'e' (abbreviation).
'cases' means one lot of letters goes inside another.
'rears'+'e'='rearse'
'he' going within 'rearse' is 'REHEARSE'.
'to' is the link.
(Other definitions for rehearse that I've seen before include "Cast practise for play" , "Practice for the performance" , "Recite - try out" , "Go over" , "Train" .)