I've probably missed a few, but...
ARABIAN LEOPARD
None in the Europe
ERMINE
Wildwood, British Wildlife Centre, Battersea Park Children's Zoo
WESTERN SPOTTED SKUNK
None in Europe
GRIZZLY BEAR
None in the UK - nearest I've seen them is Cologne
WATER MONGOOSE
I think this is a synonym for Marsh Mongoose? If so, Curraghs Isle of Man has them
SMALL SPOTTED GENET
Mablethorpe
DINGO
No Australian Dingos in the UK; closest thing would be the RSCC's Singing Dogs
ARTIC FOX
Highland, Welsh Mountain, Wildwood
BOBCAT
None in the UK - nearest would be Arnhem
SAND CAT
Bristol, Marwell
SCOTTISH WILDCAT
Twycross, Birmingham NC, Chestnut Centre, Wildwood, Port Lympne, Wingham, British Wildlife Centre, Highland (and probably a good few more)
CLOUDED LEOPARD
Howletts, Thrigby Hall (RSCC have one but typically off-show as far as I ca tell
COUGAR
Alternative name for Puma - Gentleshaw, Cromer, RSCC, Exmoor, Dartmoor
GAINT PANGOLIN
None in Europe - those Leipzig has Chinese Pangolins
GROUNDHOG
AKA Woodchuck; none in Europe
PREHENSILE – TAILED TREE PORCUPINE
Amazon World, Cotswold
VICUNA
See bongorob's post above!
MOOSE
Highland
PRONGHORN
None in Europe
YAK
Highland, Wetlands, West Mids (still there?)
GREATER KUDU
See bongorob's post again!
INDIAN BLACK BUCK ANTELOPE
...and again!
MUSK OX
None in UK - kept in quite a few European zoos - nearest would probably be Gaiapark Kerkrade
SPECLED HARE WALLABY
None in Europe
NUMBAT (BANDED ANTEATER)
None in Europe
AYE - AYE
Bristol, West Mids, Jersey, London (offshow still?), Edinburgh (until recently, not sure if still there)
OLIVE BABOON
Knowsley - probably not quite pure but close enough!
SHOEBILL
None in UK - kep a few places in Europe - closest Parc Paradiso in Belgium or Wuppertal in Germany
SCARLET IBIS
These are pretty common - most of the bird parks and many zoos have them
MARABOU STORK
As per Scarlet Ibis
GOLDEN EAGLE
Welsh Mountain certainly
STELLER’S SEA EAGLE
Edinburgh
HARPY’S EAGLE
None in UK - nearest would be Wuppertal
TAKAHE
None in Europe
HOATZIN
None in Europe
RESPLENDENT QUETZAL
None of this species in Europe that I know of - other species of quetzal turn up occasionally - Ive seen Golden-headed, Pavonine and Crested; the latter at Amazon World
YELLOW – BILLED OXPECKER
None in Europe
KOALA
Edinburgh
ARTIC WOLF
None in UK - a few on the continent but sometimes of dubious ancestry
Where I've put 'None in Europe' or 'None in UK', that's all as far as I know - if anyone knows better then feel free to correct me!
This website I think will be useful to you:
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