Put off speech about one in decline (13)
I believe the answer is:
deterioration
'decline' is the definition.
(deterioration is a kind of decline)
'put off speech about one' is the subsidiary indication.
'put off' becomes 'deter' (I've seen this before).
'speech' becomes 'oration' (oration is a kind of speech**).
'about' means one lot of letters go next to another.
'one' becomes 'i' (roman numeral).
'oration' put after 'i' is 'ioration'.
'deter'+'ioration'='deterioration'
'in' is the link.
(Other definitions for deterioration that I've seen before include "Rot!" , "A progressive worsening" , "Process of worsening" .)