Murphy turns up in the outskirts of Southend (4)
I believe the answer is:
spud
'murphy' is the definition.
('spud' can be a synonym of 'murphy')
'turns up in the outskirts of southend' is the wordplay.
'turns' is a reversal indicator.
'in the' indicates putting letters inside.
'outskirts of' suggests removing the centre.
'southend' with its centre removed is 'sd'.
'up' in reverse letter order is 'pu'.
'pu' going into 'sd' is 'SPUD'.
(Other definitions for spud that I've seen before include "Spade; potato (slang)" , "Tater" , "Weeding spade" , "One might have an eye" , "one's eyed" .)