Look for jack in outer Southgate (5)
I believe the answer is:
stare
'look' is the definition.
(stare is a kind of look)
'jack in outer southgate' is the wordplay.
'jack' becomes 'tar' (I've seen this before).
'in' is an insertion indicator.
'outer' says to hollow out the word (remove centre letters).
'southgate' with its middle taken out is 'se'.
'tar' going inside 'se' is 'STARE'.
'for' acts as a link.
(Other definitions for stare that I've seen before include "Gaze fixedly" , "Look with fixed gaze" , "Long fixed look" , "'Look fixedly, without blinking (5)'" , "bird" .)