Latvian gave permit to Middle Eastern (4)
I believe the answer is:
lett
'latvian' is the definition.
'permit to middle eastern' is the wordplay.
'permit to' becomes 'let' (I've seen this before).
'middle' indicates the central letters.
The central letter of 'eastern' is 't'.
'let'+'t'='LETT'
'gave' acts as a link.
(Other definitions for lett that I've seen before include "Balt" , "Native of Latvia" , "Baltic citizen" , "northerner" , "East European" .)