Go around a metropolis mostly tight-lipped (8)
I believe the answer is:
taciturn
'tight-lipped' is the definition.
(I've seen this before)
'go around a metropolis mostly' is the wordplay.
'go' becomes 'turn' (as in one's go or turn in a game).
'around' indicates putting letters inside.
'metropolis' becomes 'city' (a metropolis is a large city).
'mostly' means to remove the last letter.
'a'+'city'='acity'
'acity' with its last letter taken off is 'acit'.
'turn' going around 'acit' is 'TACITURN'.
(Other definitions for taciturn that I've seen before include "Reserved and uncommunicative" , "withdrawn" , "Untalkative" , "Habitually silent" , "Uncommunicative, of few words" .)