Strange glee I come across in Belgium (5)

I believe the answer is:

liege

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'in belgium' is the definition.
(I know that Belgium is a is part of of Liege)

'strange glee i' is the wordplay.
'strange' indicates an anagram.
'glee'+'i'='gleei'
'gleei' with letters rearranged gives 'LIEGE'.

'come across' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for liege that I've seen before include "On about one East Belgium city" , "European university" , "Feudal (lord); vassal" , "Belgian city or ancient lord" , "Belgian, French-speaking city" .)

I've seen this clue in The Irish News and The Globe and Mail.

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