First chases second, being tearful (5)
I believe the answer is:
moist
'tearful' is the definition.
(I've seen this in another clue)
'first chases second' is the wordplay.
'first' becomes 'ist' (ist resembles mst).
'chases' is a charade indicator (letters next to each other).
'second' becomes 'mo' (both are short periods of time).
'ist' after 'mo' is 'MOIST'.
'being' is the link.
(Other definitions for moist that I've seen before include "Dampish" , "lubricated" , "Slightly wet, damp" , "sloppy" , "bit wet" .)