Paper handkerchiefs start to trigger problems (7)
I believe the answer is:
tissues
'paper handkerchiefs' is the definition.
(I've seen this before)
'start to trigger problems' is the wordplay.
'start to' indicates taking the first letters.
'problems' becomes 'issues' (I've seen this before).
The first letter of 'trigger' is 't'.
't'+'issues'='TISSUES'
(Other definitions for tissues that I've seen before include "Paper hankies" , "Paper handkerchiefs" , "Catchers, when suffering from cold" , "Thin skins or papers" , "Soft, thin pieces of paper" .)