Maybe it's run down with a certain sign of regret (4)
I believe the answer is:
tear
'sign of regret' is the definition.
'tear' can be an answer for 'sign' (I have seen 'Sign of sorrow' mean 'tear' so perhaps 'sign' could also mean 'tear'). I'm unsure of the 'of regret' bit.
'maybe it's run down with a certain' is the wordplay.
I cannot really see how this works, but
'run' could be 'r' (cricket abbreviation) and 'r' is located in the answer.
'a' is found in the answer.
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is found in the answer.
A single letter 'e' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for tear that I've seen before include "Rip; salty drop" , "Come apart" , "wrench" , "A drop of optical moisture" , "Lacerate - sign of sorrow" .)