Chat up a Romeo in the lift, perhaps (5)
I believe the answer is:
flirt
'chat up' is the definition.
('flirt' can be a synonym of 'chat up')
'a romeo in the lift perhaps' is the wordplay.
'a romeo' becomes 'r' (phonetic alphabet: alpha, bravo, charlie etc.).
'in' means one lot of letters goes inside another.
'perhaps' is an anagram indicator.
'lift' with letters rearranged gives 'flit'.
'r' going inside 'flit' is 'FLIRT'.
(Other definitions for flirt that I've seen before include "Coquet" , "Behave playfully with opposite sex" , "Hussy" , "Dalliance" , "Engage lightheartedly in amorous banter" .)