Maybe lost dog has run away for stick (4)
I believe the answer is:
stay
'stick' is the definition.
(synonyms)
'maybe lost dog has run away' is the wordplay.
I cannot really see how this works, but
'away' could be 'a' (abbreviation as used in sports fixtures) and 'a' is present in the answer.
The remaining letters 'sty' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).
'for' is the link.
(Other definitions for stay that I've seen before include "Put off - visit" , "Supporting rope; remain" , "Check" , "lodge" , "Corset strut" .)