Make off, finding unhealthy condition around City (6)
I believe the answer is:
decamp
'make off' is the definition.
(I've seen this before)
'unhealthy condition around city' is the wordplay.
'unhealthy condition' becomes 'damp' (condition in a building).
'around' means one lot of letters goes inside another.
'city' becomes 'EC' (the City of London postcode).
'damp' placed around 'ec' is 'DECAMP'.
'finding' acts as a link.
(Other definitions for decamp that I've seen before include "Make off - from tent?" , "Depart suddenly or secretly" , "Make sudden breakaway" , "Run away (unseen)" , "Fold tents and go" .)