Game teacher raised in river out East (6)
I believe the answer is:
tigris
'river out east' is the definition.
(Middle Eastern river)
'game teacher raised' is the wordplay.
'game' becomes 'tig' (I've seen this in other clues).
'teacher' becomes 'sir' (way of addressing a male teacher).
'raised' is a reversal indicator (going up in a down clue).
'sir' written backwards gives 'ris'.
'tig'+'ris'='TIGRIS'
'in' is the link.
(Other definitions for tigris that I've seen before include "Flower of Baghdad" , "It flows through Iraq" , "Major tributary of the Euphrates" , "Great river of 30 across" , "River of Baghdad" .)