Depend on some mongrel you met (4)
I believe the answer is:
rely
'depend' is the definition.
(to depend on someone is to rely on them)
'some mongrel you met' is the wordplay.
'some' says the answer is hidden in the clue (some parts of the word are used).
'RELY' is hidden within 'mongrel you met'.
'on' acts as a link.
(Other definitions for rely that I've seen before include "Trust, depend" , "Run and see" , "Depend, bank" , "Count" , "Depend (upon)" .)