Teams in Tbilisi despairing (5)
I believe the answer is:
sides
'teams' is the definition.
(I've seen this before)
'in tbilisi despairing' is the wordplay.
'in' indicates the answer is hidden within the clue.
'SIDES' is hidden in the letters of 'tbilisi despairing'.
(Other definitions for sides that I've seen before include "More than one team" , "parties" , "Aspects" , "Teams or flat surfaces" , "Takes the part of someone in a dispute" .)