Live with a bird out in the region (5)

I believe the answer is:

tibet

I'm a little stuck... Click here to teach me more about this clue!

'the region' is the definition.
(Tibet is a region in Asia)

'live with a bird out' is the wordplay.
'live with' becomes 'be' (synonyms. I am not sure about the 'with' bit.).
'a bird' becomes 'tit' (tit is a kind of bird).
'out' is an insertion indicator.
'be' inserted into 'tit' is 'TIBET'.

'in' is the link.

Can you help me to learn more?

(Other definitions for tibet that I've seen before include "Mountainous Asian region" , "Himalayan region controlled by China" , "High place" , "far-flung highland area" , "Chinese region" .)

I've seen this clue in the Evening Standard.

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