Epitaph soon started to produce tears (4)
I believe the answer is:
rips
'tears' is the definition.
(I know this)
'epitaph soon started' is the wordplay.
'epitaph' becomes 'RIP' (rest in peace).
'started' says to take the initial letters.
The initial letter of 'soon' is 's'.
'rip'+'s'='RIPS'
'to produce' acts as a link.
(Other definitions for rips that I've seen before include "cuts" , "Tears violently" .)