Father's unlikely to be set on fire! (6)
I believe the answer is:
thames
'on fire' is the definition.
The definition suggests a singular noun which matches the answer.
'father's unlikely to be' is the wordplay.
I cannot quite see how this works, but
'be' could be 'am' and 'am' is located in the answer.
This explanation may well be incorrect...
'set' is the link.
Can you help me to learn more?
(Other definitions for thames that I've seen before include "One going to live abroad" , "Longest English river" , "River at Lechlade" , "Longest river in England" , "The Ma's in London" .)