Tipsy concierge drinking Tango in vain (10)
I believe the answer is:
egocentric
'vain' is the definition.
(thesaurus)
'tipsy concierge drinking tango' is the wordplay.
'tipsy' indicates an anagram.
'drinking' means one lot of letters goes inside another (inserted letters are consumed or drunk).
'tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'concierge' with letters rearranged gives 'egocenric'.
'egocenric' going around 't' is 'EGOCENTRIC'.
'in' acts as a link.
(Other definitions for egocentric that I've seen before include "Self-interested" , "Self-obsessed" , "Not thinking of others" , "Self-seeking" , "Selfish" .)