Irish dance was set up by one of those types cutting corners
I believe the answer is:
jig saw
'one of those types cutting corners' is the definition.
I can't judge whether this definition defines the answer.
'irish dance was set up by' is the wordplay.
'irish dance' becomes 'jig' (I've seen this before**).
'set up' says the letters should be written in reverse.
'by' says to put letters next to each other.
'was' backwards is 'saw'.
'jig'+'saw'='JIG-SAW'
Can you help me to learn more?
(Other definitions for jig saw that I've seen before include "Fragmented puzzle" , "Puzzle with pieces to assemble" , "Tools for cutting curved outlines" , "Piecing-together puzzle" , "Sharp tool (for cutting puzzle into pieces?)" .)