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Grit making up one third of island in river (6)

Ross

I believe the answer is:

tigris

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'river' is the definition.
(Tigris is an example)

'grit making up' is the wordplay.
'making' indicates anagramming the letters.
'up' becomes 'is' (I've seen this in other clues).
'grit' is an anagram of 'tigr'.
'tigr'+'is'='TIGRIS'

'one third of island in' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for tigris that I've seen before include "River of Baghdad" , "Euphrates companion river" , "Major tributary of the Euphrates" , "Flower of Baghdad" , "Baghdad's river" .)

I've seen this clue in the Sydney Morning Herald.
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